
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
Given that both $k$ and $b$ are non-zero constants, consider the following three conditions:
1) Both $\{a\_n\}$ and $\{ka\_n + b\}$ are geometric sequences;
2) $\{a\_n\}$ is an arithmetic sequence, and $\{ka\_n + b\}$ is a geometric sequence;
3) $\{a\_n\}$ is a geometric sequence, and $\{ka\_n + b\}$ is an arithmetic sequence;
Determine which of these conditions can definitely lead to the conclusion that the sequence $\{a\_n\}$ is a constant sequence. Fill in the blank with the number(s) corresponding to all applicable conditions.

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