
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 $f(x)=2\cos (\omega x+\varphi)+1$ ($\omega > 0$, $|\varphi| < \frac{\pi}{2}$), the distance between two adjacent intersection points of its graph and the line $y=3$ is $\frac{2\pi}{3}$. If $f(x) > 1$ holds for any $x\in(-\frac{\pi}{12},\frac{\pi}{6})$, determine the range of $\varphi$.

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