
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 the square $EFGH$ is shaded? All angles in the diagram are right angles, and the side length of the square is 8 units. In this square:
- A smaller square in one corner measuring 2 units per side is shaded.
- A larger square region, excluding a central square of side 3 units, occupying from corners (2,2) to (6,6) is shaded.
- The remaining regions are not shaded.

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