
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 altitude to the hypotenuse divides the hypotenuse into two segments whose difference is $e$; the difference between the two legs is $d$. What are the sides and angles of the triangle?

Example:

$$
e = 37.0488 \mathrm{~cm}, \quad d = 31 \mathrm{~cm}
$$

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