
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
Consider the sequence $\{a_n\}$. If there exists a positive integer $T$ such that $a_{n+T} = a_n$ holds for any positive integer $n$, then the sequence $\{a_n\}$ is called a periodic sequence with period $T$. Let $b_1 = m (0 < m < 1)$, and for any positive integer $n$, $b_{n+1} = \begin{cases} b_n - 1 & (b_n > 1) \\ \frac{1}{b_n} & (0 < b_n \leq 1) \end{cases}$. If the sequence $\{b_n\}$ is a periodic sequence with period $5$, then the value of $m$ can be ___. (Only one value of $m$ needs to be provided.)

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