
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 \( f(x) = x + 2 \), \( g(x) = x/3 \), and \( h(x) = x^2 \). Also denote the inverses of these functions as \( f^{-1}, g^{-1}, \) and \( h^{-1} \). Compute:
\[
f(h(g^{-1}(f^{-1}(h^{-1}(g(f^2(5)))))))
\]

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