
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
Find all function  $f:\mathbb{R}\rightarrow\mathbb{R}$  such that for all  $x,y\in\mathbb{R}$  the following equality holds \[
f(\left\lfloor x\right\rfloor y)=f(x)\left\lfloor f(y)\right\rfloor \] where  $\left\lfloor a\right\rfloor $  is greatest integer not greater than  $a.$ *Proposed by Pierre Bornsztein, France*

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