
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 \( b_{2010} = 12 + \sqrt{5} \), then determine \( b_{2023} \).

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