
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 \(ABCD\), on the extension of side \(CD\) past point \(D\), point \(E\) is marked. The angle bisector of \(\angle ABC\) intersects side \(AD\) at point \(K\), and the angle bisector of \(\angle ADE\) intersects the extension of side \(AB\) at point \(M\). Find \(BC\) if \(MK = 10\) and \(AB = 7\).

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