
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 points on $\overline{AB}$ and $\overline{BC}$ respectively such that $AD = \frac{3}{4}AB$ and $BE = \frac{1}{4}BC$. If $A=(0,8)$, $B=(0,0)$, and $C=(12,0)$, determine the area of $\triangle DBC$.

[asy]
size(200); defaultpen(linewidth(.7pt)+fontsize(10pt));
pair A, B, C, D, E, F;
A=(0,8);
B=(0,0);
C=(12,0);
D=(0,6);
E=(9,0);
F=(12/4,2);
draw(E--A--C--B--E);
draw((-1,0)--(13,0), EndArrow);
draw((0,-1)--(0,9), EndArrow);
label("$A(0,8)$", A, W);
label("$B(0,0)$", B, SW);
label("$C(12,0)$", C, S);
label("$D$", D, W);
label("$E$", E, S);
label("$F$", F, E);
label("$x$", (13,0), dir(0));
label("$y$", (0,9), dir(90));
[/asy]

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