
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 given configuration, two segments $\overline{AB}$ and $\overline{A'B'}$ are mapped to each other with $\overline{AB}$ being $5$ units long and $\overline{A'B'}$ being $8$ units long. Each segment has its midpoint, $D$ and $D'$, respectively. Let $x$ be the distance from a point $P$ on $\overline{AB}$ to $D$, and let $y$ be the distance from the associated point $P'$ on $\overline{A'B'}$ to $D'$. If $x = \lambda$ units for some point, find $x + y$ when the connectivity scheme ensures the total path (spanning through $\overline{AB}$ and connecting through to end $B'$ on $\overline{A'B'}$, via a unique point connection map) remains constant and equals the sum of the lengths of $\overline{AB}$ and $\overline{A'B'}$.
A) $6.5$
B) $5.5$
C) $7.5$
D) $8.5$
E) $9.5$

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