
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 circles, no two of which are congruent, have centers at $A$, $B$, $C$, and $D$. Points $P$ and $Q$ lie on all four circles. The radius of circle $A$ is $\tfrac{4}{7}$ times the radius of circle $B$, and the radius of circle $C$ is $\tfrac{4}{7}$ times the radius of circle $D$. It is known that $AB = 42$ and $CD = 42$, also the length of $PQ$ is 56. Let $R$ be the midpoint of $\overline{PQ}$. Calculate $\overline{AR}+\overline{BR}+\overline{CR}+\overline{DR}$.
A) 160
B) 168
C) 176
D) 184
E) 192

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