
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 the function $f(x) = 3\sin(2x + \varphi)$, where $\varphi \in (0, \pi)$, by moving its graph to the right along the x-axis by $\frac{\pi}{6}$ units to obtain the graph of function $g(x)$. If the function $g(x)$ satisfies $g(|x|) = g(x)$, then determine the value of $\varphi$.

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