
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
A math interest group studied the properties of an even function $f(x)$ and found that the function satisfies $f(x+2) = f(x) + f(1)$ over its domain $\mathbb{R}$, and it is increasing on the interval $[0, 1]$. Based on this, the group members drew the following conclusions:  
① The graph of the function $y=f(x)$ is symmetric about the line $x=1$;  
② The period of the function $y=f(x)$ is 2;  
③ When $x \in [-3, -2]$, $f′(x) \geq 0$;  
④ The points on the graph of the function $y=f(x)$ with even $x$-coordinates are all local minima of the function. Among these conclusions, the correct ones are.

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