
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
On a right-angled triangular billiard table, we hit the ball from one of the acute angle vertices along the angle bisector. The ball, after reflecting off the third side, returns to the starting vertex along the path it initially traveled. What are the magnitudes of the acute angles of the table? (The principle of elastic collision geometrically aligns with that of light reflection.)

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