
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
The monotonic increasing interval of the function $y = -\cos\left( \frac{x}{2} - \frac{\pi}{3}\right)$ is $\left[4k\pi - \frac{4}{3}\pi, 4k\pi + \frac{2}{3}\pi\right] \quad (k\in \mathbb{Z})$.

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