
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 $f(x) = \cos x$, each point on the graph has its abscissa changed to $\frac{1}{\omega}$ times the original ($\omega > 0$) while the ordinate remains unchanged. The resulting graph is then shifted to the right by $\frac{\pi}{12}$ units. Determine the minimum value of $\omega$ such that the new graph is symmetrical about the line $x = \frac{\pi}{4}$.

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