
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 a square grid of 121 points arranged in an 11 × 11 grid, two points P1 and P2 located symmetrically at (5,5) and (7,7) respectively, what is the probability that the line P1Q or P2Q is a line of symmetry for the square, where Q is one of the remaining 119 points.

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