
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 $b_1, b_2, b_3, \dots$ be a sequence of real numbers satisfying
\[b_n = b_{n-1} b_{n+1}\] for all $n \geq 2$. If $b_1 = 2 + \sqrt{5}$ and $b_{1984} = 12 + \sqrt{5}$, then determine $b_{2023}$.

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