
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 a right triangle, the segment of the perpendicular bisector of the hypotenuse that lies between the lines extended from the legs is as long as the hypotenuse. What are the angles of the triangle?

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