
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 rhombus \(ABCD\) with side length \(a\) and angle \( \angle A = 60^{\circ} \), points \(E\) and \(F\) are the midpoints of sides \(AB\) and \(CD\) respectively. Point \(K\) lies on side \(BC\), and segments \(AK\) and \(EF\) intersect at point \(M\). Find \(MK\), given that the area of quadrilateral \(MKCF\) is \(\frac{3}{8}\) of the area of rhombus \(ABCD\).

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