
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 $\{b_n\}$ be a sequence of positive numbers defined by $b_1 = b$, $b_2 = kb$, and $b_{n+2} = b_n b_{n+1}$ for all positive integers $n$. Determine under what conditions the sequence $\{b_n\}$ is a geometric progression.
A) $b = 1$ and $k = 1$
B) $b = 1$
C) $k = 1$
D) $b = k$
E) Any positive $b$ and $k$

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