
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 points $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ lie on the graph of the inverse proportion function $y=\frac{6}{x}$. <br/>$(1)$ If $\frac{x_1}{x_2}=2$, then $\frac{y_1}{y_2}=\_\_\_\_\_\_.$ <br/>$(2)$ If $x_{1}=x_{2}+2$, $y_{1}=3y_{2}$, then when the independent variable $x \gt x_{1}+x_{2}$, the range of values for the function $y$ is ______.

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