
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 two lines $l_{1}: x-y-1=0$ and $l_{2}: x+y-3=0$  
$(I)$ Find the coordinates of the intersection point $P$ of line $l_{1}$ and line $l_{2}$;  
$(II)$ A line passing through point $P$ intersects the non-negative half-axis of the $x$-axis at point $A$ and the $y$-axis at point $B$, and the area of $\triangle AOB=4$ (where $O$ is the origin), find the slope $k$ of line $AB$.

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