
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 equations with $x$ and $y$: $\left\{\begin{array}{l}{x+y-5k=0①}\\{x-y-9k=0②}\end{array}\right.$, and the solution is also a solution of the equation $2x+3y=6$. Find the value of $4k-1$.

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