
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 $a > b > 0 > c$, points $A(a-b, y_{1})$, $B(a-c, y_{2})$, $C(c-a, y_{3})$ lie on the graph of the inverse proportion function $y=\frac{k}{x}$ (where $k$ is a positive constant), the relationship between $y_{1}$, $y_{2}$, $y_{3}$ is ______. (Connect with "$>$").

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