
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 rectangle \(ABCD\), where \(AB = 6\) and \(AD = 3\left(1+\frac{\sqrt{2}}{2}\right)\), two circles are located. A circle of radius 2 with center at point \(K\) is tangent to sides \(AB\) and \(AD\). A circle of radius 1 with center at point \(L\) is tangent to side \(CD\) and the first circle. Find the area of triangle \(CLM\), where \(M\) is the foot of the perpendicular dropped from vertex \(B\) to the line passing through points \(K\) and \(L\).

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