
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
What percentage of the six-by-six square is shaded in dark grey, and what percentage is shaded in light grey? Assume the total square is divided into 36 smaller squares of equal size, and the pattern is as follows:

- Dark grey squares are at (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
- Light grey squares are at (1,2), (1,3), (2,1), (2,3), (3,1), (3,2).

[asy]
size(5cm,5cm);
for (int i = 0; i <= 60; i += 10) {
    draw((i,0)--(i,60));
    draw((0,i)--(60,i));
}
fill((0,50)--(10,50)--(10,60)--(0,60)--cycle,gray(0.7)); // (1,1)
fill((10,40)--(20,40)--(20,50)--(10,50)--cycle,gray(0.7)); // (2,2)
fill((20,30)--(30,30)--(30,40)--(20,40)--cycle,gray(0.7)); // (3,3)
fill((30,20)--(40,20)--(40,30)--(30,30)--cycle,gray(0.7)); // (4,4)
fill((40,10)--(50,10)--(50,20)--(40,20)--cycle,gray(0.7)); // (5,5)
fill((50,0)--(60,0)--(60,10)--(50,10)--cycle,gray(0.7)); // (6,6)
fill((0,40)--(10,40)--(10,50)--(0,50)--cycle,gray(0.5)); // (1,2)
fill((0,30)--(10,30)--(10,40)--(0,40)--cycle,gray(0.5)); // (1,3)
fill((10,50)--(20,50)--(20,60)--(10,60)--cycle,gray(0.5)); // (2,1)
fill((10,30)--(20,30)--(20,40)--(10,40)--cycle,gray(0.5)); // (2,3)
fill((20,50)--(30,50)--(30,60)--(20,60)--cycle,gray(0.5)); // (3,1)
fill((20,40)--(30,40)--(30,50)--(20,50)--cycle,gray(0.5)); // (3,2)
[/asy]

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