
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 line $l: y=kx-2k+1$ where $k\in \mathbb{R}$.  
$(1)$ If the line $l$ does not pass through the second quadrant, find the range of values for $k$.  
$(2)$ If the line $l$ intersects the $x$-axis and the positive $x$-axis at points $A$ and $B$ respectively, and the area of $\triangle AOB$ is $\frac{9}{2}$ (where $O$ is the origin), find the equation of the line $l$ in this case.

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