
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 $f(x)=\sin (\omega x+\varphi)$ (where $\omega > 0$, $|\varphi| < \frac{\pi}{2}$), the distance between adjacent axes of symmetry of the graph is $\frac{\pi}{2}$, and one center of symmetry is $(-\frac{\pi}{6},0)$. Determine the direction and magnitude of the horizontal shift required to obtain the graph of $g(x)=\cos \omega x$ from the graph of $f(x)$.

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