
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 $f(x) = \sin^2(wx) - \sin^2(wx - \frac{\pi}{6})$ ($x \in \mathbb{R}$, $w$ is a constant and $\frac{1}{2} < w < 1$), the graph of function $f(x)$ is symmetric about the line $x = \pi$.

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

(II) In $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $a = 1$ and $f(\frac{3}{5}A) = \frac{1}{4}$, find the maximum area of $\triangle ABC$.

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