
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 $x, y$ satisfying the inequality system $\begin{cases} 3x+y\geq 0 \\ 4x+3y \geq k \end{cases}$ and the minimum value of $z = 2x + 4y$ is $-6$, then the value of $k$ is

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