
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 an isosceles trapezoid with bases of 1 and 9, there are two circles, each of which touches the other circle, both lateral sides, and one of the bases. Find the area of the trapezoid. 

In the convex quadrilateral \(A B C D\), the points \(K, L, M, N\) are the midpoints of the sides \(A B, B C, C D, D A\) respectively. The segments \(K M\) and \(L N\) intersect at point \(E\). The areas of the quadrilaterals \(A K E N, B K E L\), and \(D N E M\) are 6, 6, and 12 respectively. Find:

a) The area of the quadrilateral \(C M E L\).

b) The length of the segment \(C D\) if \(A B=\frac{1}{2}\).

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