
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  $c\in \mathbb{R}$  such that there exists a function  $f:\mathbb{R}\to \mathbb{R}$  satisfying   $$ (f(x)+1)(f(y)+1)=f(x+y)+f(xy+c) $$   for all  $x,y\in \mathbb{R}$ .

*Proposed by Kaan Bilge*

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