
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 $f(x)=\sin \omega x-\cos \omega x$ $(\omega > \frac {2}{3})$, if the abscissa of the intersection point of any axis of symmetry of the graph of $f(x)$ with the $x$-axis does not belong to the interval $(\pi,2\pi)$, then the range of $\omega$ is \_\_\_\_\_\_ . (Express the result as an interval)

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