
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
Translate a given function $f(x)=A\sin(\omega x+\varphi)$ (with $A\neq 0$, $\omega > 0$, $-\frac{\pi}{2} < \varphi < \frac{\pi}{2}$) which is an odd function. If the graph of this function is translated left by $\frac{\pi}{6}$ units, and the resulting graph is symmetric with respect to the origin, determine the potential values of $\omega$. The options are:
A) $6$
B) $3$
C) $4$
D) $2$

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