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

$(1)$ Find the analytical expression of the function;

$(2)$ Find the range of values for which the function $f(x) \leqslant 0$.

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