
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 two points O(0,0) and Q(a,b), point P<sub>1</sub> is the midpoint of the line segment OQ, point P<sub>2</sub> is the midpoint of the line segment QP<sub>1</sub>, P<sub>3</sub> is the midpoint of the line segment P<sub>1</sub>P<sub>2</sub>, and so on, P<sub>n+2</sub> is the midpoint of the line segment P<sub>n</sub>P<sub>n+1</sub>. Find the limit position of point P<sub>n</sub>.

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