
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
If a sequence $\{a_n\}$ satisfies: there exists a positive integer $T$, such that for any positive integer $n$, $a_{n+T} = a_n$ holds, then the sequence $\{a_n\}$ is called a periodic sequence, with a period of $T$. Given that the sequence $\{a_n\}$ satisfies $a_{n+1} = \begin{cases} a_{n}-1, & a_{n} > 1 \\ \frac {1}{a_{n}}, & 0 < a_{n} \leq 1 \end{cases}$ and $a_1 = m$ ($m > 0$), the following conclusions are drawn:
1. If $m= \frac {4}{5}$, then $a_3 = 3$;
2. If $a_3 = 2$, then $m$ can take 3 different values;
3. If $m= \sqrt {2}$, then $\{a_n\}$ is a periodic sequence with a period of 3;
4. There exists $m \in \mathbb{Q}$ and $m \geq 2$, such that $\{a_n\}$ is a periodic sequence.

The correct conclusion numbers are $\boxed{\text{2, 3}}$.

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