See mull in Webster's New World Roget's A-Z Thesaurus II
verb
To think or think about carefully and at length:
chew on (or over), cogitate, consider, contemplate, deliberate, entertain, excogitate, meditate, muse1, ponder, reflect, revolve, ruminate, study, think, think out, think over, think through, turn over, weigh. Idioms: cudgel one's brains, put on one's thinking cap, rack one's brain. See thoughts
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