
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
Determine the sum of all numbers of the form \(3k+2\) where \(k\) ranges from \(0\) to \(n\), plus 5. The correct sum should be:
A) \(\frac{3n^2 + 7n + 10}{2}\) \\
B) \(\frac{3n^2 + 4n + 14}{2}\) \\
C) \(3n^2 + 7n + 14\) \\
D) \(\frac{3n^2 + 7n + 14}{2}\)

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