
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
$ABC$ is a right triangle where $\angle BAC = 90^\circ$, with $AB = 2$ cm and $AC = 1$ cm. Extend $\overline{BC}$ 2 cm to $D$ so that $CD = 2$ cm. Point $E$ is the midpoint of $\overline{AB}$, and a line from $E$ perpendicular to $\overline{AC}$ intersects $\overline{AC}$ at $F$. Determine the area of quadrilateral $BDFC$ in square centimeters.

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