
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 side length 3 cm. Extend $\overline{CD}$ by its own length to $E$, and let $F$ be the midpoint of $\overline{AB}$. Suppose $\overline{FE}$ intersects $\overline{AD}$ at point $G$. Find the area of the quadrilateral $BFGC$ in square centimeters.

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