
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
Determine the real numbers  $ a,b, $  such that  $$  [ax+by]+[bx+ay]=(a+b)\cdot [x+y],\quad\forall x,y\in\mathbb{R} ,  $$  where  $ [t] $  is the greatest integer smaller than  $ t. $ 

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