
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 function $f(x)=-\frac{3}{x}$.  
$(1)$ If the tangent line of the curve $y=f\left(x\right)$ at point $A\left(1,f\left(1\right)\right)$ intersects the $x$-axis and $y$-axis at points $M$ and $N$ respectively, find the area of $\triangle MON$ $(O$ is the origin);  
$(2)$ Find the equation of the line that is tangent to the curve $y=f\left(x\right)$ and passes through the point $\left(0,2\right)$.

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