
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
\[
\lfloor y \rfloor \cdot \{y\} = b \cdot y^2
\]
is $360$, where $\lfloor y \rfloor$ denotes the greatest integer less than or equal to $y$ and $\{y\} = y - \lfloor y \rfloor$ denotes the fractional part of $y$. What is $r + s$?
**A)** 861
**B)** 900
**C)** 960
**D)** 1021

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