
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 that four circles have centers at $A$, $B$, $C$, and $D$, and points $P$ and $Q$ lie on all four circles, with $AC = BD = 50$ and $PQ = 52$, where $R$ is the midpoint of $\overline{PQ}$, and the radius of circle $A$ is $\tfrac{5}{8}$ times the radius of circle $C$, and the radius of circle $B$ is $\tfrac{5}{8}$ times the radius of circle $D$, calculate the value of $\overline{AR}+\overline{BR}+\overline{CR}+\overline{DR}$.

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