
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 $f(x)=\sin (ωx+φ)$ where $ω > 0$ and $-\frac {π}{2} < φ < \frac {π}{2}$, determine the values of $ω$ and $φ$ such that if all points on the graph have their x-coordinates shortened to half of their original length and then shifted to the right by $\frac {π}{6}$ units, the resulting graph of $y=\sin x$ is obtained.

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