
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
62 m and n are natural numbers. A wall is a rectangle OABC with dimensions m and n units in length and width respectively. A ball starts from point O and rolls along the angle bisector of ∠AOC. When the ball hits a wall, it turns 90 degrees and continues rolling. If it encounters a vertex, it stops. Where does the ball stop?

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