
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 $y = A\sin(\omega x + \phi)$ ($A > 0$, $\omega > 0$, $\phi \in (-\frac{\pi}{2}, \frac{\pi}{2})$), whose graph passes through point $P(\frac{\pi}{12}, 0)$. The coordinates of the nearest highest point to point $P$ on the graph are $(\frac{\pi}{3}, 5)$.

(1) Find the analytical expression of the function;

(2) Find the maximum value of the function and the corresponding $x$ value;

(3) Find the range of $x$ values for which $y \leq 0$.

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