
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 \( m \) is a fixed integer greater than 1, the sequence \( x_{0}, x_{1}, x_{2}, \cdots \) is defined as follows:
$$
x_{i}=\left\{\begin{array}{ll}
2^{i}, & 0 \leqslant i \leqslant m-1, \\
\sum_{j=1}^{m} x_{i-j}, & i \geqslant m .
\end{array}\right.
$$

Find the maximum value of \( k \) such that there are \( k \) consecutive terms in the sequence which are all divisible by \( m \).

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