
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 new shaded square? Place the bottom-left vertex of the square at grid point (3,3) and the square rotates 45 degrees (square's sides are diagonals of the smaller grid cells).
```
[asy]
size(6cm);
fill((3,3)--(4,4)--(5,3)--(4,2)--cycle,gray(0.7));
dot((1,1));
for (int i = 0; i <= 6; ++i) {
    draw((0,i)--(6,i));
    draw((i,0)--(i,6));
    for (int j = 0; j <= 6; ++j) {
        dot((i,j));
    }
}
draw((3,3)--(4,4)--(5,3)--(4,2)--cycle);
[/asy]
```

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