
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 trapezoid \(ABCD\) with an area of 1, the bases \(BC\) and \(AD\) are in the ratio \(1:2\). Let \(K\) be the midpoint of the diagonal \(AC\). The line \(DK\) intersects the side \(AB\) at point \(L\). Find the area of the quadrilateral \(BCLK\).

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