
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
Let $ABCD$ be a rectangle where $AB = c$ and $AD = d$. Points $E$ and $F$ are on sides $AB$ and $AD$ respectively where $AE = AF = x$. Determine the maximum area of quadrilateral $CDFE$ in terms of $c$ and $d$.
A) $\frac{c^2 + d^2}{8}$
B) $\frac{(c + d)^2}{4}$
C) $\frac{(c + d)^2}{8}$
D) $\frac{(c - d)^2}{8}$
E) $\frac{2cd}{8}$

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