
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 a function \( f(n) \) on the set of positive integers that satisfies the following conditions:
\[ f(n) = n - 12 \quad \text{when} \quad n > 2000 \]
\[ f(n) = f(f(n + 16)) \quad \text{when} \quad n \leq 2000 \]

(1) Find \( f(n) \).

(2) Find all solutions to the equation \( f(n) = n \).

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