
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 the sequence \(\left\{a_{n}\right\}\) with the general term
\[ a_{n} = n^{4} + 6n^{3} + 11n^{2} + 6n, \]
find the sum of the first 12 terms \( S_{12} \).

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