
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
The graph of the function $f(x)=2\sin (3x+\phi)$ is shifted to the right by $\frac{\pi}{12}$ units, so the equation becomes $f(x-\frac{\pi}{12})=2\sin (3(x-\frac{\pi}{12})+\phi)$. Given that the resulting graph is symmetric about the $y$-axis, determine the smallest possible value of $|\phi|$.

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