
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 a coordinate plane, $A$, $B$, and $C$ are points at $(0, 8)$, $(0, 0)$, and $(10, 0)$, respectively. Point $D$ is the midpoint of $\overline{AB}$, and point $E$ is one-third of the way along $\overline{BC}$ from $B$ to $C$. Determine the area of $\triangle DBC$.

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