
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
What percent of square $PQRS$ is shaded, if all angles in the diagram are right angles and a triangular section within the square remains unshaded? Assume $PQRS$ is a square of side length 6. The shaded regions are altered squares within the square, where:
1. The first region encompasses coordinates $(0,0)$ to $(2,2)$.
2. A second larger region includes coordinates from $(3,0)$ to $(6,3)$.
3. The third region covers the area from $(4,4)$ to $(6,6)$.
4. An unshaded right triangle with vertices at $(6,0), (6,3), (3,3)$ remains unshaded.

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