
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
\[ f(f(x - y)) = f(x)f(y) - kf(x) + f(y) - kxy \]
for all $x, y \in \mathbb{R}$ and some constant $k \in \mathbb{R}$. Find the sum of all possible values of $f(1)$ if $f(0) = k$.

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