
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 $f(x)=\sin^2\left(\frac{5\pi}{12}-x\right)-\sin^2\left(\frac{\pi}{12}+x\right)$ is shifted to the left by $\varphi (\varphi \gt 0)$ units to obtain the graph of the function $g(x)$. If $g(x)$ satisfies $g\left(\frac{\pi}{6}-x\right)=g\left(\frac{\pi}{6}+x\right)$, calculate the minimum value of $\varphi$.

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