_{This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2023. The accepted answer to this question will be awarded a bounty worth 50 reputation.}

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This puzzle is a variant of Thermometers, but with peppermint sticks! The goal is to shade some (or no) cells on each peppermint stick so that the shaded cells in each peppermint stick form a single contiguous strand starting at the large end. The twist (see what I did there!) is that there are two colors for shading, red and green, which must alternate along each peppermint stick. The first cell on each peppermint stick may be either red or green. Numbers on the top/left of the grid define the number of red cells in each column/row, and numbers on the bottom/right of the grid define the number of green cells in each column/row.

Penpa link!

I hope you enjoy! This puzzle can be solved with constraint programming, but there is a logical path through, so no computer solutions please. The accepted answer will have the final grid, as well as the logical steps describing the solution. Please try to avoid bifurcating; contradictions are OK, but should not require more than a single sentence to describe.