
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
Four distinct circles have centers at \( A \), \( B \), \( C \), and \( D \). Two points, \( P \) and \( Q \), lie on all four circles. The radius of circle \( A \) is \( 3/4 \) times the radius of circle \( B \), and the radius of circle \( C \) is \( 3/4 \) times the radius of circle \( D \). Moreover, \( AB = CD = 50 \) and \( PQ = 60 \). Let \( R \) be the midpoint of \( \overline{PQ} \). Calculate \( \overline{AR} + \overline{BR} + \overline{CR} + \overline{DR} \).
A) 180
B) 192
C) 200
D) 208

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