
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 that the proportional function $y=kx\left(k\neq 0\right)$ intersects with the inverse proportional function $y=-\frac{5}{x}$ at points $A(x_{1}$,$y_{1})$ and $B(x_{2}$,$y_{2})$, then the value of $x_{1}y_{2}-3x_{2}y_{1}$ is ______.

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