
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
In a psychological study to test the tacit understanding between twin subjects A and B, an experiment is designed: In a two-dimensional Cartesian coordinate system, A randomly shoots a laser beam from point (1,0) towards one of the points (0,-1), (2,-1), or (4,-1), while B simultaneously shoots a laser beam from the origin towards one of the points (3,1), (3,3), or (3,9).

(I) Calculate the probability that the two laser beams are parallel.
(II) Calculate the probability that the two laser beams are perpendicular.

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