
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
Let $\overline{AB}$ have a length of 8 units and $\overline{A'B'}$ have a length of 6 units. $D$ is located 3 units away from $A$ on $\overline{AB}$ and $D'$ is located 1 unit away from $A'$ on $\overline{A'B'}$. If $P$ is a point on $\overline{AB}$ such that $x$ (the distance from $P$ to $D$) equals $2$ units, find the sum $x + y$, given that the ratio of $x$ to $y$ (the distance from the associated point $P'$ on $\overline{A'B'}$ to $D'$) is 3:2.
A) $\frac{8}{3}$ units
B) $\frac{9}{3}$ units
C) $\frac{10}{3}$ units
D) $\frac{11}{3}$ units
E) $\frac{12}{3}$ units

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