
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 \(\{b_k\}\) be a sequence of integers such that \(b_1=2\) and \(b_{m+n}=b_m+b_n+m^2n,\) for all positive integers \(m\) and \(n.\) Find \(b_{12}.\)

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