
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 $f(x)=A\sin (2x+\phi)$, $(A > 0,|\phi| < \dfrac {\pi}{2})$, for any $x$, we have $f(x)\leqslant f\left( \dfrac {\pi}{6}\right)=2$, determine the product of the maximum and minimum values of $g(x)=A\cos (2x+\phi)$ in the interval $\left[0, \dfrac {\pi}{2}\right]$.

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