
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 6 by 6 grid of points, what fraction of the larger square's area is inside the shaded square? The vertices of the shaded square are at midpoints of the grid lines along the diagonal from one edge to the central point.

[asy]
fill((1.5,1.5)--(3,3)--(4.5,1.5)--(3,0)--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((1.5,1.5)--(3,3)--(4.5,1.5)--(3,0)--cycle);
[/asy]

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