Testing Two Different Treatment Schedules of Dabrafenib and Trametinib for Skin Cancer Which Has Spread

Inclusion Criteria: * STEP 1: REGISTRATION * Patients must have histologically or cytologically confirmed stage IV or unresectable stage III BRAF V600E or BRAF V600K mutant melanoma * Patients must have BRAF V600E or BRAF V600K mutation identified by a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory; acceptable analytic techniques include but are not restricted to DNA sequencing, pyrosequencing, polymerase chain reaction (PCR), melting point assays, and immunohistochemistry * Contrast-enhanced CT scans of the neck, chest, abdomen and pelvis are required; a whole body PET/CT scan with diagnostic quality images and intravenous iodinated contrast may be used in lieu of a contrast enhanced CT of the neck, chest, abdomen and pelvis; contrast may be omitted if the treating investigator believes that exposure to contrast poses an excessive risk to the patient; patients must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; all measurable lesions must be assessed within 28 days prior to registration; tests to assess non-measurable disease must be performed within 42 days prior to registration; all disease must be assessed and documented on the Baseline Tumor Assessment Form (RECIST 1.1) * Patients must not have received a prior BRAF or MEK inhibitor * Patients with a history of brain metastases are eligible if the patient is asymptomatic with no residual neurological dysfunction and has not received enzyme-reducing anti-epi…