
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
Let the sequence \(\{a_n\}\) be defined such that \(a_1 = 3\) and \(a_{n+1} = a_n^2 - (3n - 1)a_n + 3\). Calculate the sum of the first 11 terms of the sequence \(\{a_n\}\), denoted as \(S_{11}\).

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