
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
\[kb_1 + kb_2 + kb_3 + \dots + kb_n = n^2 kb_n\] for all \(n \ge 2.\)  If \(b_{70} = 2\) and \(k=3\), find \(b_1.\)

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