
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 functions \( f: \mathbb{R} \rightarrow \mathbb{R} \) such that

\[ f(f(x) + x + y) = f(x + y) + y f(y) \]

for all real numbers \( x \) and \( y \).

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