
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 $f(x)= \sqrt{3}\sin{\omega x}+\cos{\omega x}(\omega>0)$, and $f({\alpha})=2$, $f({\beta})=0$, the minimum value of $|{\alpha}-{\beta}|$ is $\frac {\pi}{2}$. Determine the interval where $f(x)$ is monotonically increasing.

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