
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 that \( a_{1}=1 \), \( a_{2}=3 \), and \( a_{n+2}=(n+3) a_{n+1}-(n+2) a_{n} \). If for all \( m \geqslant n \), \( a_{m} \) is divisible by 9, find the smallest value of \( n \).

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