Doxorubicin and Cyclophosphamide Followed by Paclitaxel, Trastuzumab, and Lapatinib in Treating Patients With HER2/Neu-Overexpressed Breast Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed adenocarcinoma of the breast * Bilateral synchronous breast tumors allowed * Any nodal status or tumor size allowed * No stage IV disease * HER2/neu-positive disease * 3+ by IHC OR FISH-amplified * Hormone receptor status not specified PATIENT CHARACTERISTICS: * Male or female * Menopausal status not specified * ECOG performance status 0-1 * Absolute neutrophil count ≥ 1,000/mm³ * Platelet count ≥ 100,000/mm³ * Bilirubin ≤ 1.1 mg/dL * SGOT or SGPT ≤ 2.5 times upper limit of normal (ULN) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective barrier contraception during and after completion of study therapy * LVEF ≥ 50% by MUGA scan * No peripheral neuropathy \> grade 1 * No active second malignancy within the past 5 years except for adequately treated nonmelanoma skin cancer or in situ carcinoma of the cervix * No known allergy or hypersensitivity to doxorubicin hydrochloride, cyclophosphamide, paclitaxel, or other drugs formulated in Cremophor EL * No psychiatric illness or concurrent medical conditions that would preclude study treatment * No other conditions, including any of the following: * Unstable angina * Congestive heart failure * Myocardial infarction within the past 12 months * High-risk uncontrolled arrhythmias (e.g., ventricular tachycardia, high-grade AV block, or supraventricular arrhythmias that are not adequately controlled) * No QT prolongation (\> 500 ms) * No active unresolved infections * No sensitivity to E. coli derived proteins PRIOR CONCURRENT THERAPY: * Prior hormonal therapy for chemoprevention allowed * No prior trastuzumab (Herceptin®) * No prior anthracyclines * No concurrent hormonal therapy, including hormonal contraception (e.g., birth control pills or ovarian hormonal or replacement therapy) * No other concurrent chemotherapy, radiotherapy, immunotherapy, or biotherapy for breast cancer * No concurrent drugs that may prolong the QT