
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 \(ABC\) with a right angle at vertex \(B\), a segment \(BD\) is marked on the larger leg \(BC\), equal to the length of the smaller leg. Points \(K\) and \(N\) are the bases of the perpendiculars dropped onto the hypotenuse from points \(B\) and \(D\), respectively. Find the length of segment \(BK\), given that \(AK = ND = 2\).

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