
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 $f(x)$ be a function defined on $\mathbb{R}$ with a period of $2$, and for any real number $x$, it always holds that $f(x)-f(-x)=0$. When $x \in [0,1]$, $f(x)=-\sqrt{1-x^{2}}$. Determine the number of zeros of the function $g(x)=f(x)-e^{x}+1$ in the interval $[-2018,2018]$.

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