
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 $f(x) = \cos\left(x - \frac{\pi}{3}\right) - \sin\left(\frac{\pi}{2} - x\right)$,

(I) find the smallest positive period of the function $f(x)$;

(II) if $\alpha \in \left(0, \frac{\pi}{2}\right)$ and $f\left(\alpha + \frac{\pi}{6}\right) = \frac{3}{5}$, find the value of $f(2\alpha)$.

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