
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, and the sequence \( \{x_{n}\} \) be defined as follows:
\[ 
x_{i}=\left\{
\begin{array}{ll}
2^{i}, & 0 \leq i \leq m-1 ; \\
\sum_{j=1}^{m} x_{i-j}, & i \geq m .
\end{array}
\right.
\]

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

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