
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 large square quilt is composed of nine smaller squares, with four squares each divided into two right triangles. What fraction of the square quilt is shaded if three triangles and one whole square are shaded? Express your answer as a common fraction.

[asy]size(75);
fill(shift(2,1)*unitsquare,gray(.6)); // shaded whole square
fill((0,0)--(1,0)--(0,1)--cycle,gray(.6)); // shaded triangle
fill((1,1)--(2,1)--(1,2)--cycle,gray(.6)); // shaded triangle
fill((2,0)--(3,0)--(2,1)--cycle,gray(.6)); // shaded triangle
draw(scale(3)*unitsquare); // borders of the large square
for (int i=1; i<3; ++i) { draw((i,0)--(i,3)); draw((0,i)--(3,i)); } // grid lines
[/asy]

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