
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 $f(x)=2\sqrt{3}\sin (3\omega x+\dfrac{\pi }{3})(\omega > 0)$

(1) If $f (x+\theta)$ is an even function with a period of $2\pi$, find the values of $\omega$ and $\theta$;

(2) Find the maximum value of $\omega$ such that $f(x)$ is an increasing function on $(0,\dfrac{\pi }{3})$.

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