
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 that $f(x) = 2\sin(\omega x + \frac{\pi}{6})$ ($\omega > \frac{1}{4}$, $x \in \mathbb{R}$), if the abscissa of any symmetry axis of $f(x)$ intersecting the x-axis does not belong to the interval $(\pi, 2\pi)$, then the range of $\omega$ is ___.

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