
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
A rectangle $GHIJ$ covers an area of 20 square units. Line segments connect $G$ to a point $K$ on $IJ$ such that $K$ divides $IJ$ into segments of 2 units and 8 units, and $H$ to a point $L$ on $GJ$ dividing $GJ$ into segments of 1 unit and 4 units. Determine the area, in square units, of trapezoid $KHLG$.

[asy]
size(5cm,5cm);

for(int i=0; i < 5; ++i){
for(int k=0; k < 11; ++k){
draw((0,i)--(10,i));
draw((k,0)--(k,5));
} }

draw((0,0)--(2,5));
draw((8,5)--(10,0));

label("$G$",(0,0),SW);
label("$H$",(10,0),SE);
label("$I$",(10,5),NE);
label("$J$",(0,5),NW);
label("$K$",(2,5),N);
label("$L$",(8,5),N);

[/asy]

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