
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 $y$: $\left\{{\begin{array}{l}{2x+3y=k①}\\{x+4y=k-16②}\end{array}}\right.$, and it is known that the solution satisfies $x+y=8$. Find the value of $k$. (Please solve the problem using 2 methods)

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