
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
For a sequence $\{a_n\}$ of $m$ terms ($m\in\mathbb{N}^*$, $m\ge3$), where $a_i\in\{0,1\}$ ($i=1,2,3,\ldots,m$), such a sequence is called a "0-1 sequence". If there exists a positive integer $k$ ($2\le k\le m-1$) such that some sequence of $k$ consecutive terms of $\{a_n\}$ is exactly equal to another sequence of $k$ consecutive terms in $\{a_n\}$, then the sequence $\{a_n\}$ is called a "k-th order repeatable sequence". For example, for the sequence $\{a_n\}: 0, 1, 1, 0, 1, 1, 0$, since $a_1, a_2, a_3, a_4$ are exactly equal to $a_4, a_5, a_6, a_7$ respectively, the sequence $\{a_n\}$ is a "4th order repeatable sequence".
(1) Given the sequence $\{b_n\}: 0, 0, 0, 1, 1, 0, 0, 1, 1, 0$, is this sequence a "5th order repeatable sequence"? (Fill in "是" for "yes" or "不是" for "no").
(2) To ensure that all "0-1 sequences" with $m$ terms are "2nd order repeatable sequences", what is the minimum value of $m$?

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