
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 $f(x) = \sqrt{3}\cos\left(\frac{\pi}{2} - 2x\right) - 2\cos^2x + 1$  
(1) Find the smallest positive period of $f(x)$.  
(2) The graph of function $f(x)$ is translated $m$ units to the left along the x-axis, where $m > 0$, to obtain the function $g(x)$. The graph of $g(x)$ 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}
user