
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 the trapezoid \(ABCD\), the bisector of the obtuse angle \(B\) intersects the base \(AD\) at point \(K\), which is its midpoint. \(M\) is the midpoint of \(BC\) and \(AB = BC\). 

Find the ratio \(KM: BD\).

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