
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
The square quilt block shown is made from sixteen unit squares, four of which have been divided in half diagonally to form triangles. What fraction of the square quilt is shaded? Express your answer as a common fraction.

[asy]size(100);
fill(scale(4)*unitsquare,gray(.6));
path[] interior = (1,0)--(0,1)--(1,1)--cycle^^(1,1)--(2,1)--(2,2)--(1,2)--cycle^^(1,2)--(0,2)--(1,3)--cycle^^(2,1)--(2,0)--(3,1)--cycle^^(2,2)--(3,2)--(2,3)--cycle^^(3,2)--(3,1)--(4,2)--cycle^^(3,3)--(3,4)--(4,3)--cycle;
clip(interior);
draw(interior);
draw(scale(4)*unitsquare);
[/asy]

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