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

(Ⅰ) Find the analytical expression of the function and determine the interval where the function is monotonically decreasing;

(Ⅱ) When $x \in [0,\pi]$, find the maximum and minimum values of the function and the corresponding values of $x$;

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

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