
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
Given circles with centers $A$, $B$, $C$, and $D$ and points $P$ and $Q$ lying on all four circles, with the radius of circle $A$ being $\tfrac{5}{8}$ times the radius of circle $B$, and the radius of circle $C$ being $\tfrac{5}{8}$ times the radius of circle $D$, and given that $AB = CD = 39$ and $PQ = 48$, find the sum of the lengths of segments $\overline{AR}, \overline{BR}, \overline{CR},$ and $\overline{DR}$.

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