
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
Two circles touch each other at point $A$. The point opposite to $A$ on one of the circles is $B$, and on the other circle is $C$. A line rotating around point $A$ intersects the first circle at point $D$ and the second circle at point $E$. Determine the position of the line in which the area of the convex quadrilateral defined by the points $B, C, D, E$ is the largest.

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