
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
$ABCD$ is a square with diagonal $DB$. Lines $L$ and $L'$ are parallel to each other, passing through points $A$ and $C$ respectively, and perpendicular to diagonal $DB$. $E$ and $F$ are the points where lines $L$ and $L'$ intersect diagonal $DB$, such that $DE = 1$, $EF = 2$, and $FB = 1$. Calculate the area of square $ABCD$, rounded to one decimal place.
A) 7.0
B) 7.5
C) 8.0
D) 8.5

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