Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO) or to either carboplatin or paclitaxelXx_NEWLINE_xXTREATMENT: Patients with a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib dimethyl sulfoxide (DMSO), its excipients, or DMSO, are ineligible to receive treatment with trametinib DMSOXx_NEWLINE_xXTREATMENT: Patients with a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib DMSO, its excipients, or DMSO, are ineligible to receive treatment with trametinib DMSOXx_NEWLINE_xXKnown immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to the study treatments, their excipients, and/or dimethyl sulfoxide (DMSO)Xx_NEWLINE_xXKnown immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to the study treatments, their excipients, and/or dimethyl sulfoxide (DMSO)Xx_NEWLINE_xXHave a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib or excipients or to dimethyl sulfoxide (DMSO)Xx_NEWLINE_xXHave a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO), or to compounds of similar chemical or biologic composition to navitoclaxXx_NEWLINE_xXHistory of known immediate or delayed hypersensitivity reactions attributed to compounds of similar chemical or biologic composition to AT13387, dabrafenib, or trametinib, or excipients or to dimethyl sulfoxide (DMSO)Xx_NEWLINE_xXKnown immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients, or to dimethyl sulfoxide (DMSO), or to Cremophor EL (polyoxyethylated castor oil); please note, exclusion for Cremophor is unnecessary unless paclitaxel is the only agent available and the patient randomizes to the conventional therapy optionXx_NEWLINE_xXHave a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO) or to thyrotropin alpha (Thyrogen)Xx_NEWLINE_xXKnown immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to the study treatments, their excipients, and/or dimethyl sulfoxide (DMSO)Xx_NEWLINE_xXCLINICAL/LABORATORY CRITERIA: Patients must not have an immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients, or to dimethyl sulfoxide (DMSO) or other agents used in the studyXx_NEWLINE_xXHave a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO)Xx_NEWLINE_xX