
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 color each number in the set  $S = \{1, 2, ..., 61\}$  with one of  $25$  given colors, where it is not necessary that every color gets used. Let  $m$  be the number of non-empty subsets of  $S$  such that every number in the subset has the same color. What is the minimum possible value of  $m$ ?

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