
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 $y=\sin (ωx+φ)$ where $ω > 0$ and $|φ| < \dfrac {π}{2}$, the maximum value of $y$ is $1$ when $x= \dfrac {π}{4}$ and the minimum value of $y$ is $-1$ when $x= \dfrac {7π}{12}$ in the same period.
(I) Find the analytical expression of the function $y=f(x)$.
(II) What transformations should be applied to the graph of $y=\sin x$ to obtain the graph of $y=f(x)$?
(III) Find the interval(s) where the function $f(x)$ is monotonically decreasing.

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