Study With Afuresertib and Paclitaxel in Platinum Resistant Ovarian

Inclusion Criteria: 1. 1\. Female patients at least 18 years of age at the time of signing the informed consent form and capable of giving written informed consent, which includes willingness to comply with the requirements and restrictions listed in the consent form. 2. Must provide informed consent for the procedures and the tests for PI3K/AKT/PTEN pathway alterations, BRCA1/2 mutations, and/or level of phospho-AKT. The archival tumor biopsy sample collected less than 1 year is preferred. If no archival tumor sample is available, fresh biopsy will be recommended. For patients who cannot provide a tumor sample or cannot accept fresh tumor biopsy, the Sponsor should be consulted about their qualification to enter this study. 3. Patients must have histologically or cytologically confirmed high grade serous OC, endometroid OC, or ovarian clear cell carcinoma (including fallopian tube and primary peritoneal cancers). Carcinosarcoma, sarcoma, mucinous OC, or low-grade serous OC or the other histologies must be excluded. 4. Must not have previously received prior AKT or PI3K pathway or mTOR inhibitors. 5. Must have PROC (including fallopian tube and primary peritoneal carcinoma), defined as disease relapsed between 1 to 6 months after the last dose of the first-line platinum-based therapy (at least 3 cycles), or progressed during or relapsed within 6 months of the last dose of platinum-based 2nd-5th line therapies. 6. The OC patients must have received 1 to 5 prior chemotherapies including no more than one chemotherapy after PROC was diagnosed. Combination therapy with two or more drugs will be considered as one therapy, whereas maintenance therapy will be considered as continuation of the previous systemic treatment. 7. Patients should be appropriate candidates for treatment with single agent weekly paclitaxel based on investigator's clinical assessment. 8. Eastern Cooperative Oncology Group (ECOG) Performance Status 0-2 9. Must meet the following criteria for hematology parameters: * Absolute neutrophil count (ANC) ≥ 1,500/mm3 * Platelets ≥ 100,000/µL * Hemoglobin ≥ 9.0 g/dL 10. Total serum bilirubin ≤ 1.5 × upper limit of normal (ULN) (in patients with known Gilbert's syndrome, total bilirubin ≤ 3 × ULN with direct bilirubin ≤ 1.5 × ULN). 11. Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) must be \< 2.5 × institutional ULN. For patients with liver metastasis, AST/ALT must be \< 5.0 × institutional ULN. 12. Creatinine within 1.5 × ULN or creatinine clearance \> 30 mL/min by Cockcroft Gault formula (Appendix 1). 13. Toxicities of prior therapy (except alopecia) should have been resolved to less than or equal to grade 1 as per NCI-CTCAE v5.0. 14. Patients must have GI functions that would allow absorption of afuresertib. 15. Patient must have a life expectancy of greater than 6 months. 16. Must have at least one lesion that meets the definition of measurable disease by RECIST 1.1 criteria (Appendix 3). 17. Patients of childbearing potential must agree to use adequate contraception (barrier method of birth control or abstinence) prior to study entry and for the duration of study participation. If a woman becomes pregnant or suspects she is pregnant while participating in this study, she should inform her treating physician immediately. 18. Must be off strong inhibitors or inducers of CYP3A4/5 treatment, as showed in Appendix 2, for at least 2 weeks from Study Day 1. Exclusion Criteria: 1. 1\. Primary platinum refractory disease, defined as "disease progression during or relapsed within 1 month after the last dose of the first-line platinum based therapy". 2. Known or suspected brain metastases. 3. Receiving any other anticancer therapeutic agents other than study medicines. 4. Uncontrolled ascites. 5. Known symptomatic or impending cord compression, except if the patient has received definitive treatment for this and demonstrates evidence of clinically stable disease. 6. Presence of other active cancer within 3 years prior to enrollment (other than basal cell or squamous cell skin cancer, or any other cancer in situ currently in complete remission). 7. History of seizure or condition that may predispose to seizure that needs anti-epileptic medications; brain arteriovenous malformation; or intracranial masses, such as schwannomas and meningiomas that are causing edema or mass effect. 8. Known allergies, hypersensitivity, or intolerance to the excipients of afuresertib (for excipient information, refer to the IB17). 9. Any condition for which, in the opinion of the investigator, participation would not be in the best interest of the patient (eg, compromise well-being) or that could prevent, limit, or confound the protocol-specified assessments. 10. Any medical contraindication to the use of paclitaxel. 11. Prior radiotherapy ≤ 15 days prior to Study Day 1, with the exception of a single fraction of radiotherapy for the purposes of palliation, which is permitted. 12. History of clinically significant ventricular arrhythmias (eg, ventricular tachycardia, ventricular fibrillation, or torsade de pointes). 13. Prolonged corrected QT interval by the Fridericia's correction formula (QTcF) on the screening ECG \> 470 msec. Receiving concomitant medications known to prolong QTc, or which are associated with torsade de pointes, and are unable to discontinue use while receiving study drug. 14. History or evidence for any of the following: severe or unstable angina, myocardial infarction, symptomatic congestive heart failure, arterial or venous thromboembolic events (eg, pulmonary embolism, cerebrovascular accident including transient ischemic attacks) within 6 months prior to Study Day 1 or New York Heart Association Class III to IV heart disease. 15. Presence of uncontrolled hypertension (systolic blood pressure \[BP\] \> 160 mmHg or diastolic BP \> 100 mmHg). Patients with a history of hypertension are allowed, provided that BP is controlled to within these limits by anti-hypertensive treatment. 16. Human immunodeficiency virus (HIV)-positive patients with 1 or more of the following: 1. Not receiving highly active antiretroviral therapy 2. Receiving antiretroviral therapy that may interfere with the study drug (consult the Sponsor for review of medication prior to enrollment) 3. CD4 count \< 350 based on a test within 3 months of the screening visit 4. An acquired immunodeficiency syndrome-defining opportunistic infection within 6 months of the start of screening 17. Had a major surgery ≤ 30 days prior to first study treatment at Cycle 1 Day 1. 18. Presence of grade \> 2 neuropathy. 19. Prior receipt of chemotherapy, PARP inhibitor, bevacizumab, or investigational therapy within 28 days of enrollment or within 5 half lives of the agent, whichever is shorter. 20. Patients who are pregnant or lactating. 21. Patients with high risk of tuberculosis infection, based on investigator's clinical assessment, will be screened by tuberculosis screening test, such as the QuantiFERON® TB Gold In Tube test (QFT-GIT) or the T-SPOT®.TB test (T-Spot). 22. Patients with active hepatitis B (positive hepatitis B surface antigen \[HBsAg\] test at screening) or hepatitis C (positive hepatitis C virus \[HCV\] antibody test at screening) are not allowed to be enrolled in this study. Note: * Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as having a negative HBsAg test and a positive hepatitis B core antibody \[HBcAb\] test) are eligible. * Patients positive for HCV antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA.