
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
Given the system of linear equations in two variables $x$ and $y$: $\left\{\begin{array}{l}x+2y=-a+1\\ x-3y=4a+6\end{array}\right.$ (where $a$ is a constant), if the value of the algebraic expression $kx-y$ (where $k$ is a constant) remains unchanged regardless of the value of $a$, then $k=\_\_\_\_\_\_$.

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