
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
A rectangular pool table has vertices at \((0,0)\), \((12,0)\), \((0,10)\), and \((12,10)\). There are pockets only in the four corners. A ball is hit from \((0,0)\) along the line \(y=x\) and bounces off several walls before eventually entering a pocket. Find the number of walls that the ball bounces off of before entering a pocket.

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