
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 $\{a_n\}$ of $m$ terms ($m \in N^*$, $m \geq 3$), where $a_i \in \{0, 1\}$ ($i=1, 2, \ldots, m$). If there exists a positive integer $k$ ($2 \leq k \leq m-1$), and there are two sets of consecutive $k$ terms in the sequence $\{a_n\}$ that exactly match in order, 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 $a_1, a_2, a_3, a_4$ and $a_4, a_5, a_6, a_7$ match in order, the sequence $\{a_n\}$ is a "4th order repeatable sequence". Assuming that the sequence $\{a_n\}$ is not a "5th order repeatable sequence", if one more item, either 0 or 1, is added after the last item $a_m$, making the new sequence a "5th order repeatable sequence", and given $a_4 \neq 1$, the last item of the sequence $\{a_n\}$, $a_m$, is $\boxed{\text{1}}$.

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