
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
The number \( b = \frac{r}{s} \), where \(r\) and \(s\) are relatively prime positive integers, has the property that the sum of all real numbers \(y\) satisfying
\[
\lfloor y \rfloor \cdot \{y\} = b \cdot y^{2.5}
\]
is \(315\), where \(\lfloor y \rfloor\) and \(\{y\}\) have their usual meanings. Find \(r + s\).
A) 256
B) 277
C) 315
D) 355

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