
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 $ABCD$ is shaded, where all angles in the diagram are right angles? Square $ABCD$ has a side length of 6 units. The shaded areas are formed by squares with the following configurations:
1. A square in the corner $A$, 2 units on each side.
2. A rectangle starting from the bottom left edge extending right 2 units and upward 5 units, then covering rightwards and upwards to fill a 4x4 square from the bottom.
3. A square in the top right corner of $ABCD$, extending downward and leftward to fill a 6x6 area.
[asy]
import graph;
defaultpen(linewidth(0.7));
xaxis(0,7,Ticks(1.0,NoZero));
yaxis(0,7,Ticks(1.0,NoZero));

fill((0,0)--(2,0)--(2,2)--(0,2)--cycle);
fill((0,0)--(2,0)--(2,5)--(0,5)--(0,4)--(4,4)--(4,2)--(2,2)--cycle);
fill((6,0)--(6,6)--(0,6)--(0,5)--(5,5)--(5,0)--cycle);

label("$A$",(0,0),SW);
label("$B$",(0,6),N);
label("$C$",(6,6),NE);
label("$D$",(6,0),E);
[/asy]

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