
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 graph of the function $y = g(x)$ is symmetric to the graph of the function $f(x) = a^{x-1}$ with respect to the line $y = x$, and it is given that $g(4) = 2$. Find the value of $g(2)$.

A) $-\frac{1}{2}$
B) $\frac{3}{2}$
C) $2$
D) $4$

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