
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 seen in the diagram is constructed from 16 smaller unit squares. Four of these small squares are diagonally split into two equal triangles. If only the triangles are shaded, and each triangle covers half of its respective square, what fraction of the large square is shaded? 

[asy]
size(100);
filldraw((0,0)--(1,0)--(0,1)--cycle, gray(0.6));  // shaded triangle in the bottom left square
filldraw((3,3)--(4,3)--(3,4)--cycle, gray(0.6));  // shaded triangle in the top right square
filldraw((3,0)--(4,0)--(4,1)--cycle, gray(0.6));  // shaded triangle in the bottom right square
filldraw((0,3)--(0,4)--(1,4)--cycle, gray(0.6));  // shaded triangle in the top left square
draw((0,0)--(4,0)--(4,4)--(0,4)--cycle);  // large square
draw((1,0)--(1,4));  // vertical lines
draw((2,0)--(2,4));
draw((3,0)--(3,4));
draw((0,1)--(4,1));  // horizontal lines
draw((0,2)--(4,2));
draw((0,3)--(4,3));
[/asy]

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