
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 $EFGH$ is shaded? All angles in the diagram are right angles. Consider square $EFGH$ with side length 6 units. Shaded areas are defined as follows:
1. A rectangle from (0,0) to (2,2).
2. A rectangle from (3,0) to (6,6), but only the region below y=x-3.
3. A right triangle with vertices at (0,6), (6,6), and (0,0).

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