
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 $y = A\sin(\omega x + \varphi)$ $(A > 0, \omega > 0, |\varphi| < \frac{\pi}{2})$ whose graph passes through point $P\left(\frac{\pi}{12}, 0\right)$, and the nearest highest point to $P$ on the graph is $Q\left(\frac{\pi}{3}, 5\right)$.

(1) Find the expression of the function;

(2) Indicate the increasing interval of the function;

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

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