
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 vectors $\overrightarrow{OP\_1}$, $\overrightarrow{OP\_2}$, and $\overrightarrow{OP\_3}$ that satisfy the equation $\overrightarrow{OP\_1} + \overrightarrow{OP\_2} + \overrightarrow{OP\_3} = 0$, and have magnitudes $|\overrightarrow{OP\_1}| = |\overrightarrow{OP\_2}| = |\overrightarrow{OP\_3}| = 1$, find the magnitude of vector $\overrightarrow{P\_1P\_2}$.

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