
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 \( Q \) lie in a plane with \( PQ = 10 \). How many locations for point \( R \) in this plane are there such that the triangle with vertices \( P \), \( Q \), and \( R \) is a right triangle with area \( 16 \) square units?
A) 2
B) 4
C) 6
D) 8
E) 12

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