
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
Define the function $f(n)$ on the positive integers such that $f(f(n)) = 3n$ and $f(4n + 2) = 4n + 3$ for all positive integers $n$. Find $f(1000)$.

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