
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
Let the set \( A = \{1, 2, 3, 4, 5, 6, 7\} \). The function \( f: A \rightarrow A \) is bijective and satisfies \( f(f(f(x))) = x \) for \( x \in A \). Find the number of such mappings \( f \).

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