
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
Find all functions  $f:\mathbb{R} \to \mathbb{R}$  such that  $f(x)\geq 0\ \forall \ x\in \mathbb{R}$ ,  $f'(x)$  exists  $\forall \ x\in \mathbb{R}$  and  $f'(x)\geq 0\ \forall \ x\in \mathbb{R}$  and  $f(n)=0\ \forall \ n\in \mathbb{Z}$ 

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