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An oscillating multi-tool absolutely crushes both jobs - the blade gets into tight corners for trim work way better than a utility knife, and for caulk removal it'll save you hours of scraping! The only thing is you'll want to grab a proper caulk removal blade since the standard ones don't work quite as well on that task.

For caulk removal specifically, the oscillating multi-tool is solid, but grab a decent carbide or oscillating caulk blade - the cheap ones clog up fast and you'll waste time cleaning them. On trim work it depends on what you're doing; it's great for undercutting door jambs and getting into gaps, though you'll still want a sharp utility knife handy because the multi-tool blade can sometimes chip brittle trim if you're not careful with pressure.

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