
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
Resize the horizontal coordinate of every point on the graph of the function $f(x) = \sin(\omega x + \phi)$, where $\omega > 0$ and $- \frac{\pi}{2} < \phi < \frac{\pi}{2}$, to half of its original size while keeping the vertical coordinate unchanged, then shift the graph to the right by $\frac{\pi}{4}$ units to obtain the graph of $y = \sin x$. Compute $f\left( \frac{\pi}{6} \right)$.

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