
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
One evening, 21 people made phone calls, and it was discovered that these 21 people made a total of $n$ calls, with each pair of people making at most one call. Additionally, it was noted that there exists a group of $\mathrm{m}$ people where the 1st person called the 2nd person, the 2nd person called the 3rd person, $\cdots$, the $(\mathrm{m}-1)$th person called the $\mathrm{m}$th person, and the $\mathrm{m}$th person called the 1st person. The value of $\mathrm{m}$ is an odd number. Find the minimum value of $n$ such that no matter the calling situation, there must exist a group of 3 people among these 21 people who have all called one another.

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