
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
There are $5 \cdot 338$ singers participating in an arts festival, and you need to schedule $m$ performances, with 4 singers performing in each. Ensure that any two of the 8 singers perform together the same number of times. Design a schedule that minimizes the number of performances $m$.

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