
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 \(ABC\), height \(CD\) is dropped from the vertex of the right angle \(C\). The projection of segment \(BD\) on leg \(BC\) is \(l\), and the projection of segment \(AD\) on leg \(AC\) is \(m\). Find the hypotenuse \(AB\).

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