
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 $\mathbb{R}$ such that for any real number $x$, it always satisfies $f(x+2)=f(-x)$, $f(x)=-f(4-x)$, and when $x\in[0,2]$, $f(x)=2x-x^2$.
(1) Find the analytic expression of $f(x)$ when $x\in[2,4]$;
(2) Calculate the sum $f(0)+f(1)+f(2)+\cdots+f(2019)$.

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