
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 the leg \( BC \) of the right triangle \( ABC \), a circle is constructed with \( BC \) as the diameter. The circle intersects the hypotenuse at point \( D \) such that \( AD : BD = 1 : 3 \). The altitude from vertex \( C \) (the right angle) to the hypotenuse is 3. Find the leg \( BC \).

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