
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
Given a function $f(x)$ defined on $\mathbb{R}$, for any $a, b \in \mathbb{R}$, it satisfies $f(a + b) = f(a) + f(b) - 1$. When $x > 0$, $f(x) > 1$; and $f(2) = 3$.
1. Find the values of $f(0)$ and $f(1)$.
2. Determine the monotonicity of the function $f(x)$ on $\mathbb{R}$ and provide a proof.
3. If $f(-kx^2) + f(kx - 2) < 2$ holds for any $x \in \mathbb{R}$, find the range of values for the real number $k$.

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