
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
Let $f(x) : \mathbb{R} \to \mathbb{R}$ be a function such that
\[
\frac{f(x) f(y) - f(xy)}{2} = x + y + 1
\]
for all $x,$ $y \in \mathbb{R}.$ Find $f(x)$.

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