
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
In a mapped segment diagram, $\overline{CD}$ is 10 units long with midpoint $E$, and $\overline{C'D'}$ is 16 units long with midpoint $E'$. A point $Q$ is situated 3 units from $E$ towards $D$ on $\overline{CD}$. If $Q'$ on $\overline{C'D'}$ is associated with $Q$, and the segments are associated in a manner such that the distance from the start of one segment to a point is half the distance from the start of the second segment to the associated point, find the total distance $x + y$. Here $x$ is the distance from $Q$ to $E$ and $y$ is the distance from $Q'$ to $E'$.
A) 6
B) 7
C) 9
D) 10

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