
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
On the rectangular coordinate plane, a point \( P \) is randomly chosen on the line segment joining \((0, -1)\) and \((0, 1)\). Another point \( Q \) is randomly chosen on the line segment joining \((1, -1)\) and \((1, 1)\). Two circles, each with radius 1, are then drawn using \( P \) and \( Q \) as centers respectively. Find the probability that the two circles intersect.

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