
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 $f(x) = A\sin(wx + \frac{\pi}{6})$ ($A > 0$, $w > 0$) has a minimum positive period of $\pi$, and when $x \in [0, \frac{\pi}{2}]$, the maximum value of $f(x)$ is 4,
1. Find the value of $A$;
2. Find the interval of monotonic increase of the function $f(x)$ on $[-\pi, 0]$.

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