
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
Translate the function $f(x)=\sin^2x-2\sin x\cos x+3\cos^2x$ by $m(m>0)$ units to the left along the $x$-axis to obtain the function $g(x)$. If the graph of $g(x)$ is symmetric about the line $x=\frac{\pi}{8}$, determine the minimum value of $m$.

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