
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 quadrilateral $ABCD$, find a point $E$ such that the ratio of the areas of triangles $EAB$ and $ECD$ is $1:2$, and the ratio of the areas of triangles $EAD$ and $EBC$ is $3:4$, given the coordinates of its vertices: $A(-2, -4)$, $B(-2, 3)$, $C(4, 6)$, $D(4, -1)$.

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