
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 new linear mapping setup, segment $\overline{AB}$ of length 10 units is mapped to segment $\overline{A'B'}$ which is 5 units long. If $D$ and $D'$ are the respective midpoints of $\overline{AB}$ and $\overline{A'B'}$, and if $x$ is the distance from a point $P$ on $\overline{AB}$ to $D$, while $y$ is the distance from the associated point $P'$ on $\overline{A'B'}$ to $D'$, find the value of $x + y$ when $x = 3$ units.

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