
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 terms of the sequence $(b_i)$ defined by $b_{n + 2} = \frac{b_n + 4060}{3 + b_{n + 1}}$ for $n \ge 1$ are integers. Determine the minimum possible value of $b_1 + b_2$ where $b_1$ and $b_2$ are positive.

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