
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 quadrilateral ABCD where AB ∥ CD and AD ∥ BC, creating a rectangle, AB = 1, BC = 2. Let E be the centroid of triangle BCD. If F is a point on DA such that DF = (1/4)DA, calculate the ratio of the area of triangle DFE to the area of quadrilateral ABED.

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