
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 square with side length 2. Points $E$ and $F$ are marked respectively on sides $AB$ and $AD$ such that $AE = AF = x < 1$. A point $G$ on side $BC$ satisfies $BG = x$. Determine $x$ that maximizes the area of the pentagon $CDFEG$.
A) 1.0
B) 1.25
C) 1.5
D) 1.75

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