
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 real function  $f$  is defined for  $\forall$   $x\in \mathbb{R}$  and  $f(0)=0$ . Also  $f(9+x)=f(9-x)$  and  $f(x-10)=f(-x-10)$  for  $\forall$   $x\in \mathbb{R}$ . What’s the least number of zeros  $f$  can have in the interval  $[0;2014]$ ? Does this change, if  $f$  is also continuous?

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