
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
Two circles, $X$ and $Y$, have centers at points $M$ and $N$ respectively, and points $U$ and $V$ lie on both circles. The radius of circle $X$ is $\tfrac{3}{4}$ times the radius of circle $Y$, and $MN = 63$. Furthermore, if $W$ is the midpoint of $\overline{UV}$ and segment $\overline{UV} = 60$, find $\overline{MW}+\overline{NW}$.
A) 45
B) 56
C) 63
D) 70
E) 78

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