
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 $f(x)=A\sin (ωx+φ),x∈R(A > 0,ω > 0,0 < φ < \dfrac{π}{2})$, the distance between two adjacent intersection points of the graph with the $x$-axis is $\dfrac{π}{2}$, and there is a minimum point $M( \dfrac{2π}{3},-2)$ on the graph.

1. Find the analytical expression of the function $f(x)$ and its monotonically decreasing interval.
2. Find the range of $f(x)$ when $x∈\[ \dfrac{π}{12}, \dfrac{π}{2}\]$.

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