
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
A function $y=\sin (ωx+φ)(ω > 0,|φ| < \dfrac {π}{2})$ in the same period has a maximum value of $1$ when $x= \dfrac {π}{4}$ and a minimum value of $-1$ when $x= \dfrac {7π}{12}$.
(1) Find the analytical expression of the function $y=f(x)$.
(2) How can the graph of the function $y=\sin x$ be transformed to obtain the graph of $y=f(x)$?
(3) If the function $f(x)$ satisfies the equation $f(x)=a(0 < a < 1)$, find the sum of all the real roots in $[0,2π]$.

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