
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 \( f : \mathbb{R} \to \mathbb{R} \) be a function such that
\[ f(f(x + y)) = f(x)f(y) + f(x) + f(y) + xy \]
for all \( x, y \). Find the sum of all possible values of \( f(1) \).

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