
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
Several  fleas sit on the squares of a  $10\times 10$  chessboard (at most one  fea per square). Every minute, all  fleas simultaneously jump to adjacent squares. Each  fea begins jumping in one of four directions (up, down, left, right), and keeps jumping in this direction while it is possible; otherwise, it reverses direction on the opposite. It happened that during one hour, no two  fleas ever occupied the same square. Find the maximal possible number of  fleas on the board.

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