
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 the center of a rectangular billiard table with a length of 3 meters and a width of 1 meter, there is a billiard ball. It is struck in a random direction and stops exactly 2 meters away. Find the expected number of reflections off the edges of the table.

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