
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 strictly positive integer, and let \( r_{1}, \ldots, r_{m} \) be rational numbers such that \( r_{1} + \ldots + r_{m} = 1 \). What are the minimum and maximum values attained by the function \( f(n) = n - \sum_{i=1}^{m} \left\lfloor r_{i} n \right\rfloor \) for \( n \in \mathbb{N}^{*} \)?

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