
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
Yasha and Grisha are playing a game: first, they take turns naming a number from 1 to 105 (Grisha goes first, and the numbers must be different). Then each counts the number of different rectangles with integer sides whose perimeter equals the named number. The player with the higher number of rectangles wins. What number should Grisha name to win? Rectangles that differ only by rotation are considered the same. For example, rectangles $2 \times 3$ and $3 \times 2$ are considered the same.

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