
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 $f(x) = \sqrt{3}\sin{2x} - \cos{2x}$, determine the range of the positive number $a$ such that the graph of the function is monotonically increasing in the intervals $\left[0, \frac{a}{3}\right]$ and $\left[2a, \frac{4\pi}{3}\right]$.

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