
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
Define \( S_n = \{0, 1, \cdots, n-1\} \) where \( n \in \mathbf{Z}_{+} \).

For a bijection \( f: S_n \rightarrow S_n \), if \( n \mid (a+b-c) \) for \( a, b, c \in S_n \), then
\[ n \mid (f(a) + f(b) - f(c)). \]

Let the set of all such functions \( f \) be \( T_n \). If \( \left| T_n \right| = 60 \), find \( n \).

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