
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 $\{b_n\}$ is defined by $b_1 = 1$ and $3^{b_{n+1} - b_n} - 1 = \frac{1}{n + 1}$ for $n \geq 1$. Find the least integer $k > 1$ for which $b_k$ is an integer.

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