
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
In the Cartesian coordinate system, the graph of a linear function intersects the $x$-axis at point $A(-1,0)$ and the $y$-axis at point $B(0,-2)$.  
$(1)$ Find the analytical expression of the linear function.  
$(2)$ If there is a point $C$ on the line $AB$, and the area of $\triangle BOC$ is $4$, write down the coordinates of point $C$: ______.

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