
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 lengths of two adjacent sides of a rectangle are $8$ and $x$, the perimeter is $y$, and the area is $S$.  
$(1)$ The relationship between $y$ and $x$ is: ______;  
$(2)$ The relationship between $S$ and $x$ is: ______;  
$(3)$ When $S=80$, find the value of $y$.

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