
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

There are 12 shapes made from matches - 3 triangles, 4 squares, and 5 pentagons. The shapes do not share sides. Petya and Vasya take turns removing one match at a time. Vasya wants as few untouched shapes as possible to remain, while Petya wants as many untouched shapes as possible to remain. How many shapes will remain after 10 turns? Each player makes 5 moves, and Petya starts first.

Present the answer in LaTex format: \boxed{Your answer}
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