
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
Given a power function $f(x) = x^{a}$ whose graph passes through the fixed point that the function $g(x)=m^{x-2} - \frac{1}{2}$ ($m > 0$ and $m \neq 1$) goes through, find the value of $f(\frac{1}{3})$.

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