
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 real function $f$ has the property that for any positive integers $a, b, n$ such that $a + b = 3^n$, the equation
\[ f(a) + f(b) = 2n^2 \]
holds. What is $f(242)$?

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