
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 the function $f(x)=\frac{1}{2}\cos(ωx+φ)$ for any $x\in\mathbb{R}$, it satisfies $f(\frac{π}{3}-x)=f(\frac{π}{3}+x)$. If the function $g(x)=3\sin(ωx+φ)-2$, find the value of $g(\frac{π}{3})$.

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