
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
\[ b_1 + b_2 + b_3 + \dots + b_n = n^3 b_n \] for all \( n \geq 2 \). If \( b_{50} = 2 \), find \( b_1 \).

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