
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
Calculate the arithmetic mean (average) of the squares of the first $n$ positive integers. What is this mean?
A) $\frac{n(n+1)}{6}$  
B) $\frac{n(n+1)(2n+1)}{6}$  
C) $\frac{(n+1)(2n+1)}{6}$  
D) $\frac{(n+1)(n+2)}{6}$  
E) $\frac{(n+1)(n+2)}{3}$
A) $\frac{n(n+1)}{6}$  
B) $\frac{n(n+1)(2n+1)}{6}$  
C) $\frac{(n+1)(2n+1)}{6}$  
D) $\frac{(n+1)(n+2)}{6}$  
E) $\frac{(n+1)(n+2)}{3}$

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