
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 $b_1 = 3 + \sqrt{2}$ and $b_{2021} = 7 + 2\sqrt{2},$ determine $b_{2050}.$

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