
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 percent of the six-by-six square is shaded?

[asy]
size(6cm,6cm);
for (int i = 0; i < 6; ++i)
    for (int j = 0; j < 6; ++j)
        if ((i + j) % 2 == 0) fill((10*i,10*j)--(10*i,10*(j+1))--(10*(i+1),10*(j+1))--(10*(i+1),10*j)--cycle,gray(0.7));
draw((0,0)--(0,60),black);
draw((0,60)--(60,60),black);
draw((60,60)--(60,0),black);
draw((60,0)--(0,0),black);
for (int i = 1; i <= 6; ++i) {
    draw((10*i,0)--(10*i,60), black);
    draw((0,10*i)--(60,10*i), black);
}
[/asy]

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