
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 $O$, $A$, $B$ not on the same line, and point $P$ is a point on the plane, determine the relationship between the position of point $P$ and the line segment $AB$ if $2 \overrightarrow{OP} = 2 \overrightarrow{OA} + 2 \overrightarrow{OB}$.

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