
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
Given the convex quadrilateral $ABCD$, a line starting from the diagonal $BD$ moves parallel to its initial position towards the vertex $C$, intersecting $CB$ at $E$ and $CD$ at $F$. At what position of the line will the area of triangle $AEF$ be the largest?

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