
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  $f : (0, \infty) \to \mathbb{R}$  is differentiable such that  $\lim \limits_{x \to \infty} f(x)=2019$  Then which of the following is correct?
[list=1]
[*]  $\lim \limits_{x \to \infty} f'(x)$  always exists but not necessarily zero.
[*]  $\lim \limits_{x \to \infty} f'(x)$  always exists and is equal to zero.
[*]  $\lim \limits_{x \to \infty} f'(x)$  may not exist.
[*]  $\lim \limits_{x \to \infty} f'(x)$  exists if  $f$  is twice differentiable.
[/list]

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