
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 all integers $n \geq 7,$ evaluate the expression:
\[
\frac{(n+3)! + (n+1)!}{(n+2)!}
\]
A) $(n+3) + \frac{1}{n+2}$
B) $\frac{n^2 + 5n + 6}{n+2}$
C) $\frac{n^2 + 5n + 7}{n+2}$
D) $\frac{n^2 + 5n + 8}{n+2}$

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