
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
Shift the graph of $f(x) = \cos \omega x$ ($\omega > 0$) to the right by $\frac{\pi}{3}$ units to get the graph of the function $y = g(x)$. If $y = g(x)$ is an odd function, then determine the minimum value of $\omega$.

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