
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 $10$-cm-by-$12$-cm rectangle is partitioned as shown. Points $A$ and $B$ are located 3 cm from the top side and 3 cm from the bottom side, respectively, on opposite sides of the rectangle. What is the area of the shaded region?

[asy]
draw((0,0)--(15,0));
draw((15,0)--(15,12));
draw((15,12)--(0,12));
draw((0,12)--(0,0));
draw((0,0)--(7.5,12));
draw((7.5,12)--(15,0));
draw((0,12)--(7.5,0));
draw((7.5,0)--(15,12));
fill((7.5,0)--(11.25,6)--(7.5,12)--(3.75,6)--cycle,gray);
label("A",(7.5,12),N);
label("B",(7.5,0),S);
[/asy]

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