
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, the drummers stand in an even square formation of 50 rows by 50 drummers. The drummers are dressed in either blue or red costumes. What is the largest number of drummers that can be dressed in blue costumes such that each drummer dressed in blue can only see drummers in red costumes? Consider the drummers to be looking in all directions (360 degrees) and as point-like.

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