
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 \(a_{1}=1\) and \(a_{2}=3\), for all positive integers \(n\), we have
\[ 
a_{n+2} = (n+3)a_{n+1} - (n+2)a_{n}.
\]
Find all values of \(a_{n}\) that are divisible by 11.

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