
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 arranged in a 4x4 grid. Some of these unit squares are divided diagonally into two triangles, and half of these triangles are shaded. If exactly two whole squares are fully shaded, and four squares are divided into two shaded triangles such that they form another square, what fraction of the quilt is shaded? Express your answer as a common fraction.

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