
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
A trapezoid \(KLMN\) is inscribed in a circle with center \(O\), where \(KN \parallel LM\), \(KN = 6\), \(LM = 4\), and \(\angle KLM = 135^\circ\). Point \(A\) lies on segment \(KN\), and \(AK = 4\). Find the distance from point \(O\) to line \(BN\).

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