
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, $G$ and $H$ are the midpoints of $\overline{JK}$ and $\overline{KL}$ respectively. If $J$ is at $(0,8)$, $K$ is at $(0,0)$, and $L$ is at $(10,0)$, determine the area of $\triangle GKL$.

[asy]
size(180); defaultpen(linewidth(.7pt)+fontsize(10pt));
pair J, K, L, G, H;
J=(0,8);
K=(0,0);
L=(10,0);
G=(0,4);
H=(5,0);
draw(H--J--L--G);
draw((-1,0)--(11,0), EndArrow);
draw((0,-1)--(0,9), EndArrow);
label("$J(0,8)$", J, W);
label("$K(0,0)$", K, SW);
label("$L(10,0)$", L, S);
label("$G$", G, W);
label("$H$", H, S);
[/asy]

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