
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
Assume that $e$, $f$, $g$, and $h$ are positive integers such that $e^5 = f^4$, $g^3 = h^2$, and $g - e = 31$. Determine $h - f$.

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