
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 the function $f(x)$, defined on $\mathbb{R}$, satisfy: for any real numbers $x$ and $y$, $f(x+y)=f(x)+f(y)$ holds, and $f(-1)=2$. When $x > 0$, $f(x) < 0$ always holds.  
$(1)$ Find the values of $f(0)$ and $f(2)$;  
$(2)$ If the inequality $f(t^{2}+3t)+f(t+k) \leqslant 4$ always holds for $t \in \mathbb{R}$, find the range of values for $k$.

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