
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 the sequence $\{a_n\}$ satisfies $a_1=m(m > 0)$, $a_{n+1}= \begin{cases} a_n-1, & a_n > 1 \\ \frac{1}{a_n}, & 0 < a_n \leqslant 1 \end{cases}$, with $a_3=4$, determine the set of all possible values of $m$.

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