
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
Let \( m \) be a fixed integer greater than 1. The sequence \( x_0, x_1, x_2, \ldots \) is defined as follows:
$$
x_i = \begin{cases} 
2^i, & 0 \leq i \leq m-1 ; \\
\sum_{j=1}^{m} x_{i-j}, & i \geq m .
\end{cases}
$$

Find the maximum value of \( k \) such that the sequence contains \( k \) consecutive terms all divisible by \( m \).

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