
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 $f(x) = 3\sin{\frac{x}{2}} - 2\cos{\frac{x}{2}}$, the graph of the function $y = f(x)$ is translated right by $\frac{\pi}{3}$ units to obtain the graph of the function $y = g(x)$. If the maximum value of the function $g(x)$ is $g(\theta)$, find the value of $\cos{\left(\theta + \frac{\pi}{6}\right)}$.

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