
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 $f(x)=A\sin (\omega x+ \phi ), (x\in R, A > 0, \omega > 0, 0 < \phi < \dfrac{\pi }{2})$ with a period of $\pi$, and one of its lowest points on the graph being $M(\dfrac{2}{3}\pi ,-2)$.

(1) Find the analytic expression of $f(x)$;

(2) Find the maximum and minimum values of $f(x)$ when $x\in [0,\dfrac{\pi }{12}]$.

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