
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 $f(x)=\sin (\omega x+\frac{\pi }{3}),\ (\omega > 0)$, if $f(\frac{\pi }{6})=f(\frac{\pi }{3})$ and $f(x)$ has a maximum value but no minimum value in the interval $(\frac{\pi }{6},\frac{\pi }{3})$, calculate the value of $\omega$.

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