
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
A rectangle has length $AC = 40$ and width $AE = 25$. Point $B$ is the midpoint of $\overline{AC}$, making $AB = BC = 20$, but point $F$ is now three-fifths of the way along $\overline{AE}$ from $A$ to $E$, making $AF = 15$ and $FE = 10$. Find the area of quadrilateral $ABDF$.

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