
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, for $\angle C$ to be the largest angle of the triangle, it must be that $p < y < q$. What is the least possible value of $q - p$, expressed as a common fraction?
[asy]
draw((0,0)--(1,0)--(.4,.5)--cycle);
label("$C$",(.4,.5),N); label("$A$",(1,0),SE); label("$B$",(0,0),SW);
label("$y+6$",(.5,0),S); label("$y+3$",(.7,.25),NE); label("$2y$",(.2,.25),NW);
[/asy]

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