
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
The negation of the proposition "There exists some $x_0 \in \mathbb{R}$ such that $f(x_0) < 0$" is 
$$
\begin{align*}
\text{A}: & \exists x_0 \notin \mathbb{R}, f(x_0) \geq 0 \\
\text{B}: & \forall x \notin \mathbb{R}, f(x) \geq 0 \\
\text{C}: & \forall x \in \mathbb{R}, f(x) \geq 0 \\
\text{D}: & \forall x \in \mathbb{R}, f(x) < 0
\end{align*}
$$

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