
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 $y=\sin (ωx+φ)(ω > 0,|φ | < \dfrac{π }{2})$ in the same period, when $x=\dfrac{π }{4}$, $y$ takes the maximum value $1$, and when $x=\dfrac{7π }{12}$, $y$ takes the minimum value $-1$.

(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 the interval $[0,2π]$.

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