
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
Assume a square ABCD. Points P and Q are located one third along AB from A, and two thirds along BC from B, respectively. What fraction of the interior of the square is shaded if the region inside the square but outside the triangle APQ is shaded?

[asy]
filldraw((0,0)--(3,0)--(3,3)--(0,3)--(0,0)--cycle,gray,linewidth(1));
filldraw((0,1)--(2,3)--(3,3)--(0,1)--cycle,white,linewidth(1));
label("P",(0,1),W);
label("Q",(2,3),N);
[/asy]

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