
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
Determine the value of $k$ such that the segments $\overline{A'B'}$ and $\overline{X'Y'}$ are parallel on the Cartesian plane, where $A'(-6,0)$, $B'(0,-6)$, $X'(0,12),$ and $Y'(18,k)$.

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