
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
On some cells of a 10x10 board, there is a flea. Every minute, the fleas jump simultaneously, each one to a neighboring cell (adjacent by side). Each flea jumps strictly in one of the four directions parallel to the board's sides and maintains this direction as long as possible; otherwise, it changes to the opposite direction. Barbos the dog observed the fleas for an hour and never saw two fleas on the same cell. What is the maximum number of fleas that could have been jumping on the board?

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