
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 \( r_{1}, \ldots, r_{m} \) be positive rational numbers such that \( r_{1} + \cdots + r_{m} = 1 \). Define \( f(n) = n - \sum \left\lfloor r_{i} n \right\rfloor \). What are the minimal and maximal values taken by \( f(n) \)?

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