
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
For every composite positive integer $n$, define $r(n)$ to be the sum of the products of each prime in the factorization of $n$ and its corresponding exponent incremented by one. What is the range of the function $r$, $\{r(n): n \text{ is a composite positive integer}\}$?

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