
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 rectangle \(ABCD\), point \(E\) is marked on the extension of side \(CD\) beyond point \(D\). The bisector of angle \(ABC\) intersects side \(AD\) at point \(K\), and the bisector of angle \(ADE\) intersects the extension of side \(AB\) at point \(M\). Find \(BC\), given that \(MK = 9\) and \(AB = 4\).

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