
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 $m \geq 12,$ analyze the value of
\[\frac{(m+3)!-(m+1)!}{m!}\]
Determine if this value is always which of the following?
- (Without choices until the solution is derived)
A) A multiple of 3
B) A multiple of 15
C) A polynomial of degree 3
D) A perfect square
E) A perfect cube

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