First step locked candidate (pointing/claiming) which eliminates R4C3<>2.

Second step x-wing R16C16 which eliminates R3C1<>1 and R4C6<>1.

What I can see as next step is a skyscraper at R13C1 and R14C6 linked by row 1 which eliminates R3C4<>4 and R4C3<>4, or as alternative a w-wing at R3C1 and R4C6 linked by 2's at row 6 which eliminates R3C4<>4 and R4C3<>4. Any other possibilities I have overlooked? After this solves with singles.

begin:

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`.5623.........3.5..6.3.........3564.`

after basics:

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`.5623.3...65..3.5656.3..6..5.3.3564.`