
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 points $P_{1}$, $P_{2}$, $P_{3}$ on circle $O$, if $\overrightarrow{OP_{1}} + \overrightarrow{OP_{2}} + \overrightarrow{OP_{3}} = \overrightarrow{0}$, calculate the measure of $\angle P_{1}P_{2}P_{3}$.

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