
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

Dima and Vlad play a game: first, they take turns naming a number from 1 to 97 (Dima goes first, and the numbers must be different). Then, each counts the number of distinct rectangles with integer sides whose perimeter is equal to the named number. The winner is the one with the greater number of rectangles. Which number should Dima name to win? Rectangles that differ by rotation are considered the same. For example, the rectangles $2 \times 3$ and $3 \times 2$ are identical.

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