
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
In the triangle shown, what is the positive difference between the greatest and least possible integral values of \(y\)?

[asy]
defaultpen(linewidth(0.7));
pair a,b,c;
b = (1,2); c = (3,0);
draw(a--b--c--a);
label("$y$",a--b,dir(135)); label("7",b--c,dir(45)); label("9",c--a,S);
[/asy]

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