
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
Consider two segments $\overline{AB}$ and $\overline{A'B'}$ where $AB = 3$ units and $A'B' = 5$ units. Both segments are aligned such that points $A$ and $A'$, and $B$ and $B'$ lie on parallel lines. Let $D$ and $D'$ be the midpoints of $\overline{AB}$ and $\overline{A'B'}$, respectively. For a point $P$ on $\overline{AB}$ where $x = \text{distance}(P, D)$, we associate it with a point $P'$ on $\overline{A'B'}$ such that the function $\frac{y}{x} = \frac{5}{3}$ holds, where $y = \text{distance}(P',D')$. Calculate the value of $x+y$ when $x = 2$.
- **A)** $\frac{16}{3}$
- **B)** $\frac{15}{3}$
- **C)** $\frac{14}{3}$
- **D)** $\frac{17}{3}$

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