
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 conditions $x + y - 4 \leqslant 0$, $x - 2y + 2 \leqslant 0$, and $kx - y + 1 \geqslant 0$, where $k > \frac{1}{2}$, find the range of $k$ if the minimum value of the objective function $z = x - y$ is greater than $-3$.

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