
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 $f(x) = \cos(\omega x - \frac{\pi}{3}) - \cos(\omega x)$ $(x \in \mathbb{R}, \omega$ is a constant, and $1 < \omega < 2)$, 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 $f(\frac{3}{5}A) = \frac{1}{2}$, find the maximum area of $\triangle ABC$.

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