
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 $\overline{CD}$, where $A$ and $C$ are at position $0$ on their respective lines, and $B$ and $D$ are at positions $6$ and $9$, respectively. Let $x$ be the distance from a point $P$ on $\overline{AB}$ to $A$, and $y$ be the distance from the associated point $Q$ on $\overline{CD}$ to $C$. These distances are related such that when $x = 3k$ (where $k$ is a constant), $x + y$ equals $12k$. Determine the value of $k$.
A) $1$
B) $1.5$
C) $2$
D) $2.5$
E) $3$

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