
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 inverse proportion function $y=\frac{k}{x}(k≠0)$ passes through the point $A(-2,4)$.  
$(1)$ Find the expression of this inverse proportion function.  
$(2)$ If $B(1,y_{1})$ and $C(3,y_{2})$ are two points on the graph of this inverse proportion function, compare the values of $y_{1}$ and $y_{2}$, and explain the reason.

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