
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
Positive integers are grouped in the following way: {1}, {2, 3, 4}, {5, 6, 7, 8, 9}, {10, 11, 12, 13, 14, 15, 16}, ... Let the sum of the numbers in the nth group be denoted as $A_n$. An array is formed with the cubes of natural numbers in the following manner: {$0^3, 1^3$}, {$1^3, 2^3$}, {$2^3, 3^3$}, {$3^3, 4^3$}, ... Let the difference between the latter and the former number in the nth group be denoted as $B_n$. Then, find the expression for $A_n+B_n$.

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