
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
At the parade, drummers stand in a perfect square formation of 50 rows with 50 drummers each. The drummers are dressed either in blue or red uniforms. What is the maximum number of drummers that can be dressed in blue uniforms so that each drummer in blue sees only red drummers? Consider the drummers as looking in all directions (360 degrees) and as point-like.

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