
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
Given a sequence composed of odd numbers, where the nth group contains n numbers, 2n-1, 2n+1, ..., 4n-1, find the relationship between the sum of the numbers in each group and the group's index number n.

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