
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
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 $y=f(x)$?

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