
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
Define the sequence $(b_i)$ by the recurrence relation $b_{n+2} = \frac{b_n + 2213}{2 + b_{n+1}}$ for $n \geq 1$. Suppose all terms $b_i$ are positive integers. Determine the smallest possible value of $b_1 + b_2$.

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