
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 $\sum_{i=1}^{k} a_{m+i}$ denote the sum of $k$ consecutive terms of the sequence $a_{1}, a_{2}, \cdots, a_{n}$, where $m, k \in \mathbf{N}$, $k \geqslant 1$, $m+k \leqslant n$. Find the number of groups of consecutive terms in the sequence $1, 2, \cdots, 100$ whose sum is a multiple of 11.

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