
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 $y=A\sin({\omega x+\varphi})$ ($A>0$, $\omega>0$, $|\varphi|\leq \frac {\pi}{2}$), its graph passes through point $P(\frac {\pi}{12},0)$, and the coordinates of the nearest highest point to point P are $(\frac {\pi}{3},5)$.
(1) Find the analytical expression of the function;
(2) Find the minimum value of the function and write out the set of corresponding $x$ values;
(3) Find the range of the function when $x\in[0,\frac {\pi}{2}]$.

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