
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 sequence \(b_n\) satisfies the relation
\[ b_n = \frac{n^2 - 1}{n^2 + 1} \cdot b_{n - 1} \] for all \(n \geq 2\).
Given \(b_{50} = 2,\) find \(b_1.\)

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