
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
The sequence  $ (a_{n})_{n\geq 1}$  is defined by  $ a_{1} \equal{} 1, a_{2} \equal{} 3$ , and  $ a_{n \plus{} 2} \equal{} (n \plus{} 3)a_{n \plus{} 1} \minus{} (n \plus{} 2)a_{n}, \forall n \in \mathbb{N}$ . Find all values of  $ n$  for which  $ a_{n}$  is divisible by  $ 11$ .

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