
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, $n$ is a positive integer, and $\angle A > \angle B > \angle C$.  How many possible values of $n$ are there? [asy]
draw((0,0)--(1,0)--(.4,.5)--cycle);
label("$A$",(.4,.5),N); label("$B$",(1,0),SE); label("$C$",(0,0),SW);
label("$3n + 16$",(.5,0),S); label("$4n - 2$",(.7,.25),NE); label("$3n + 11$",(.2,.25),NW);
[/asy]

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