
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
Given the set \( A = \{1, 2, \dots, 6\} \), define a function \( f: A \rightarrow A \) such that for any \( x \in A \), we have \( f^{(0)}(x) = x \). Determine the number of functions \( f \) that satisfy this condition. Here, \( f^{(1)}(x) = f(x) \) and \( f^{(n-1)}(x) = f(f^{(n)}(x)) \) for \( n = 1, 2, \dots \).

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