
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
Alex drew a geometric picture by tracing his plastic right triangle four times, each time aligning the shorter leg with the hypotenuse and matching the vertex of the acute angle with the vertex of the right angle. It turned out that the "closing" fifth triangle was isosceles (see the drawing, specifically marked sides are equal). Find the acute angles of Alex's triangle?

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