
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 $0 \leq \theta < 2\pi$, find the maximum length of the vector $\overrightarrow{P_{1}P_{2}}$, where $\overrightarrow{P_{1}P_{2}} = (2 + \sin\theta - \cos\theta, 2 - \cos\theta - \sin\theta)$.

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