
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 two segments $\overline{AB}$ and $\overline{A'B'}$ of lengths 6 units and 16 units, respectively, points on $\overline{AB}$ and $\overline{A'B'}$ are paired in such a way that if a point $P$ on $\overline{AB}$ lies 1 unit from $A$ (and hence 5 units from $B$), the associated point $P'$ on $\overline{A'B'}$ lies 3 units from $A'$ (and 13 units from $B'$). If for a given point $P$ located $a$ units from $A$, find $x + y$ where $x$ is the distance of $P$ to $A$ and $y$ is the distance of the associated point $P'$ to $A'$.
A) $\frac{20}{5}a$
B) $\frac{18}{5}a$
C) $\frac{24}{5}a$
D) $\frac{15}{5}a$
E) $\frac{13}{5}a$

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