
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
Given a function $f(x)$ defined on $R$ such that $f(x+2)=f(x)$, and when $x\in [-1,1]$, $f(x)=e^{1-|x|}-2$. Four statements are made about the function $f(x)$: ① $f(x)$ is an even function; ② The graph of $f(x)$ is symmetric about the line $x=2$; ③ The equation $f(x)=1-|x|$ has two distinct real roots; ④ $f(\frac{1}{2}) < f(\frac{22}{3})$. The correct statements are indicated by the numbers ____.

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