
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
For a function $f(x)= \sqrt{3}\cos\left(\frac{3\pi}{2}-x\right)\sin\left(x- \frac{\pi}{2}\right)+\cos^2\left(\frac{\pi}{2}+x\right) - \frac{1}{2}$:
(I) Determine the intervals where $f(x)$ is monotonically increasing;
(II) In $\triangle ABC$, where $A$, $B$, $C$ are the angles opposite sides $a$, $b$, $c$ respectively, given that $f(A)=1$ and $a=2$, find the maximum area of $\triangle ABC$.

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