
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 a sequence $\{a\_n\}$ that satisfies: there exists a positive integer $T$ such that for any positive integer $n$, $a_{n+T}=a_{n}$ holds. The sequence $\{a\_n\}$ is called a periodic sequence with a period of $T$. It is known that the sequence $\{a\_n\}$ satisfies $a_{n+1}= \begin{cases} a_{n}-1, & a_{n} > 1 \\\\ \frac {1}{a_{n}}, & 0 < a_{n}\leqslant 1\\end{cases} a_{1}=m(m > 0)$, and 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 $m∈Q$ and $m\geqslant 2$ such that the sequence $\{a\_n\}$ is a periodic sequence.

Determine the correct conclusion(s) number(s).

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