
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 $f(x) = \sqrt{3}\sin(\omega x + \varphi)$, where $\omega > 0$ and $|\varphi| < \frac{\pi}{2}$, whose graph passes through point $A(0, \frac{3}{2})$, and points $B$ and $C$ are adjacent maximum and minimum points on the graph, respectively. If $|BC| = 4$, determine the interval on which the function $f(x)$ is monotonically increasing.

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