
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
In certain cells of a rectangular board of size 101 by 99, there is a turtle in each cell. Every minute, each turtle simultaneously crawls to an adjacent cell of the board, sharing a side with the one they are currently in. Each subsequent move is made perpendicular to the previous one: if the previous move was horizontal - left or right, then the next one will be vertical - up or down, and vice versa. What is the maximum number of turtles that can move indefinitely on the board such that at each moment no cell contains more than one turtle?

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