
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 that $0 \leqslant \phi < \pi$, the function is defined as $f(x) = \frac{\sqrt{3}}{2} \cos(2x + \phi) + \sin^2 x$.
(1) If $\phi = \frac{\pi}{6}$, find the interval where $f(x)$ is monotonically increasing.
(2) If the maximum value of $f(x)$ is $\frac{3}{2}$, find the value of $\phi$.

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