
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 \(K L M N\) is inscribed in a circle with center \(O\), where \(K L\) is parallel to \(M N\), \(K L = 8\), \(M N = 2\), and the angle \(\angle N K L\) is \(45^{\circ}\). The chord \(M A\) of the circle intersects the segment \(K L\) at point \(B\) such that \(K B = 3\). Find the distance from point \(O\) to the line \(A K\).

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