
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
Points $P$ and $Q$ are midpoints of two adjacent sides of a rectangle with length $l$ and width $w$. What fraction of the interior of the rectangle is shaded? Consider the triangle formed by the vertex at the intersection of uncut sides and points $P$ and $Q$ to be unshaded.

[asy]
filldraw((0,0)--(4,0)--(4,2)--(0,2)--(0,0)--cycle,gray,linewidth(1));
filldraw((0,1)--(2,2)--(4,2)--(0,1)--cycle,white,linewidth(1));
label("P",(0,1),W);
label("Q",(2,2),N);
[/asy]

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