
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 that $0 \leqslant \theta < 2 \pi$, two vectors are defined as $\overrightarrow{OP\_1} = (\cos \theta, \sin \theta)$ and $\overrightarrow{OP\_2} = (2 + \sin \theta, 2 - \cos \theta)$. Determine the maximum length of the vector $\overrightarrow{P\_1P\_2}$.

A) $\sqrt{2}$
B) $\sqrt{3}$
C) $3\sqrt{2}$
D) $2\sqrt{3}$

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