
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
Given an isosceles trapezoid \(ABCD\) with \(AD = 10\), \(BC = 2\), and \(AB = CD = 5\). The angle bisector of \(\angle BAD\) intersects the extension of the base \(BC\) at point \(K\). Find the angle bisector of \(\angle ABK\) in triangle \(ABK\).

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