
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
How many integer values of \( n \) make the expression (1) an integer? How many positive integer values of \( n \) make the value of \( K \) a positive integer?

$$
K=\frac{2610+201 n+110 n^{2}-n^{3}}{10+n}
$$

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