
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
Right triangle $PQR$ with right angle at $Q$ is constructed outwards on the hypotenuse $\overline{PR}$ of isosceles right triangle $OPR$ with leg length $2$. Triangle $OPR$ and triangle $PQR$ share the same perimeter. What is $\sin(2\angle OQP)$?
A) 0  
B) $\frac{1}{2}$  
C) $\frac{\sqrt{2}}{2}$  
D) $\frac{3}{4}$  
E) $\frac{\sqrt{3}}{2}$

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