
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 a 7 by 7 grid of points, what fraction of the larger square's area is inside the shaded square? The shaded square is formed by connecting four points: one at the center of the grid, and three others each one unit away horizontally, vertically, and diagonally.

[asy]
fill((3,3)--(4,4)--(3,5)--(2,4)--cycle,gray(0.7));
dot((0,0));
dot((0,1));
dot((0,2));
dot((0,3));
dot((0,4));
dot((0,5));
dot((0,6));
dot((1,0));
dot((1,1));
dot((1,2));
dot((1,3));
dot((1,4));
dot((1,5));
dot((1,6));
dot((2,0));
dot((2,1));
dot((2,2));
dot((2,3));
dot((2,4));
dot((2,5));
dot((2,6));
dot((3,0));
dot((3,1));
dot((3,2));
dot((3,3));
dot((3,4));
dot((3,5));
dot((3,6));
dot((4,0));
dot((4,1));
dot((4,2));
dot((4,3));
dot((4,4));
dot((4,5));
dot((4,6));
dot((5,0));
dot((5,1));
dot((5,2));
dot((5,3));
dot((5,4));
dot((5,5));
dot((5,6));
dot((6,0));
dot((6,1));
dot((6,2));
dot((6,3));
dot((6,4));
dot((6,5));
dot((6,6));
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