
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
The function $g(n)$ is defined on the positive integers such that $g(g(n)) = 3n$ and $g(3n + 2) = 3n + 1$ for all positive integers $n$. Find $g(243)$.

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