
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 $n \ge 2.$ If $b_1 = 2 + \sqrt{19}$ and $b_{2023} = 23 + \sqrt{19}$, then determine $b_{2076}.$

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