
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 $f(n)=\left\{\begin{array}{ll}n-12 & n>2000 ; \\ f[f(n+14)] & n \leqslant 2000\end{array}(n \in \mathbf{N})\right.$. Find all fixed points of $f(n)$.

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