
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 two geometric sequences $\{a_n\}$ and $\{b_n\}$ with the same number of terms, and $c$ is a non-zero constant. Now, construct the following four sequences:
1. $\{a_n+b_n\}$;
2. $\left\{\frac{a_n}{b_n}\right\}$;
3. $\{a_n+c\}$;
4. $\{a_n+cb_n\}$.

Among these, the sequence(s) that must be a geometric sequence is __________.

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