
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
We have a 99x99 checkerboard. There is a fly on each square. In one step, each fly must move exactly one square diagonally (multiple flies can end up on the same square). After one step, what is the minimum number of empty squares?

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