
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 circular billiard table has a diameter of 2 meters. A small elastic ball placed at point \( P \), which is \( 40 \, \text{cm} \) from the center, is struck such that it passes through \( P \) again after two reflections. Continuing the path of the ball, how far will it be from \( P \) after the tenth reflection?

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