
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 $k \in \mathbb{R}$ and $k \neq 1$, for the lines $l_1: y= \frac{k}{2}x+1$ and $l_2: y= \frac{1}{k-1}x-k$.

(1) Find the necessary and sufficient condition for $l_1 \parallel l_2$.

(2) When $x \in [-1, 2]$, the line $l_1$ is always above the x-axis, find the range of $k$.

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