
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 $f(x)$ be a function defined on the domain of all real numbers ($\mathbb{R}$), such that for all real numbers $x$ and $y$, the equation $f(x+y) = f(x) + f(y)$ holds true. Additionally, $f(-1) = 2$, and for all $x > 0$, we have $f(x) < 0$.  
(1) Find the values of $f(0)$ and $f(2)$.  
(2) Given that the inequality $f(t^2 + 3t) + f(t + k) \le 4$ holds for all real numbers $t$, determine the range of values for $k$.

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