
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
In a rectangle $ABCD$, a line segment $PR$ is drawn dividing the rectangle such that triangle $APR$ and triangle $PBC$ are congruent right triangles with vertex $P$ on side $AB$ and vertex $R$ on side $CD$. How many right triangles can be drawn using three of the points $\{A, P, R, B, C, D\}$ as vertices?
[asy]
draw((0,0)--(6,0)--(6,3)--(0,3)--cycle);
draw((2,3)--(4,0));
label("D",(0,0),S);
label("R",(4,0),S);
label("C",(6,0),S);
label("B",(6,3),N);
label("P",(2,3),N);
label("A",(0,3),N);
[/asy]

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