
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
On this 7 by 7 grid of points, what fraction of the larger square's area is inside a shaded rhombus centered within the grid, where each side of the rhombus aligns with two points diagonally spaced apart (like the previous problem, but bigger grid)?

[asy]
size(180);
fill((3,3)--(4,4)--(3,5)--(2,4)--cycle,gray(0.7));
for(int i=0; i<=6; ++i){
for(int j=0; j<=6; ++j){
dot((i,j));
}
}
draw((0,0)--(6,0)--(6,6)--(0,6)--cycle);
draw((3,3)--(4,4)--(3,5)--(2,4)--cycle);
[/asy]

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