
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
In the sequence $\{a\_n\}$, if for any $n∈N^{∗}$, there is $\frac{a_{n+2}}{a_{n+1}} - \frac{a_{n+1}}{a_{n}} = t$ (where $t$ is a constant), then the sequence $\{a\_n\}$ is called a ratio-difference sequence, and $t$ is called the ratio-common difference. Given the following propositions:
1. Geometric sequences are always ratio-difference sequences, but arithmetic sequences are not necessarily ratio-difference sequences;
2. If the sequence $\{a\_n\}$ satisfies $a\_n = \frac{2^{n-1}}{n^{2}}$, then the sequence $\{a\_n\}$ is a ratio-difference sequence, and the ratio-common difference $t = \frac{1}{2}$;
3. If the sequence $\{c\_n\}$ satisfies $c_1 = 1$, $c_2 = 1$, and $c_n = c_{n-1} + c_{n-2} (n ≥ 3)$, then the sequence is not a ratio-difference sequence;
4. If $\{a\_n\}$ is an arithmetic sequence and $\{b\_n\}$ is a geometric sequence, then the sequence $\{a\_n b\_n\}$ is a ratio-difference sequence.
The sequence number(s) of all true propositions is $\_\_\_\_\_\_\_$.

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