
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 $f\left(x\right)=\sin \left(ωx+φ\right)\left(ω > 0,-\frac{π}{2}\leqslant φ < \frac{π}{2}\right)$, each point on the graph has its x-coordinate shortened to half of its original length while the y-coordinate remains unchanged. Then, the graph is shifted to the right by $\frac{π}{6}$ units to obtain the graph of $y=\sin x$. Find the value of $f\left(\frac{π}{6}\right)$:

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