
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 function \( f(n) \) defined on the set of natural numbers \(\mathbf{N}\), and satisfies:

\[
\begin{array}{l}
f(1) = f(2) = 1, \\
f(3n) = 3 f(n) - 2, \\
f(3n+1) = 3 f(n) + 1, \\
f(3n+2) = 3 f(n) + 4 \quad (n \in \mathbf{N}).
\end{array}
\]

Determine the largest positive integer \( n \) less than or equal to 1992 for which \( f(n) = n \).

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