
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
In the diagram, $D$ and $E$ are midpoints of $\overline{AB}$ and $\overline{BC}$ respectively. Point $F$ is located such that $\overline{DF}$ is perpendicular to $\overline{BC}$, and $F$ lies on $\overline{BC}$. Given $A(0,10)$, $B(0,0)$, and $C(10,0)$, calculate the area of quadrilateral $DBCF$.

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