
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 $ABCD$, segment $RS$ divides the rectangle into two congruent rectangles. Determine how many right triangles can be formed using three of the points $\{A, R, B, C, S, D\}$ as vertices. [asy]
draw((0,0)--(10,0)--(10,4)--(0,4)--cycle);
draw((5,0)--(5,4));
label("D",(0,0),S);
label("S",(5,0),S);
label("C",(10,0),S);
label("B",(10,4),N);
label("R",(5,4),N);
label("A",(0,4),N);
[/asy]

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