
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
Given a real number  $t\neq -1$ . Find all functions  $f:\mathbb{R}\rightarrow\mathbb{R}$  such that 
\[(t+1)f(1+xy)-f(x+y)=f(x+1)f(y+1)\]
for all  $x,y\in\mathbb{R}$ .

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