
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 that point $E$ is the midpoint of side $\overline{BC}$ in square $ABCD$, and $\overline{DE}$ meets diagonal $\overline{AC}$ at $F$, determine the area of square $ABCD$ if the area of quadrilateral $DFEC$ is $36$.

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