
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 $f(x) = \sin 2x + \sin \left(2x - \frac{\pi}{3}\right)$.  
(1) Find the smallest positive period of $f(x)$.  
(2) If the graph of $f(x)$ is translated $m$ units to the left along the x-axis (where $m > 0$), the graph of the resulting function $g(x)$ is symmetric about the line $x = \frac{\pi}{8}$. Find the minimum value of $m$ and the range of $g(x)$ on $\left[0, \frac{\pi}{4}\right]$ when $m$ is at its minimum.

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