
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
Suppose that \( f(x) \) and \( g(x) \) are functions which satisfy \( f(g(x)) = x^2 \) and \( g(f(x)) = x^4 \) for all \( x \ge 1 \). If \( g(16) = 16 \), then compute \( [g(4)]^4 \).

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