
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 $f(x)=\cos x\cdot \cos (x-\theta )-\frac{1}{2}\cos \theta$, where $\theta\in(0,\pi)$. It is known that $f(x)$ reaches its maximum value when $x=\frac{\pi }{3}$.

(1) Find the value of $\theta$;

(2) Given $g(x)=2f(\frac{3}{2}x)$, find the maximum value of the function $g(x)$ on the interval $[0,\frac{\pi }{3}]$.

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