
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 the function $f(x)$ be an even function defined on $\mathbb{R}$, and for any $x \in \mathbb{R}$, it always holds that $f(x + 1) = -f(x)$. It is known that when $x \in [0, 1]$, $f(x) = 3^x$. Then

① 2 is a period of $f(x)$;  
② The maximum value of the function $f(x)$ is 1, and the minimum value is 0;  
③ The function $f(x)$ is increasing on the interval $(2, 3)$;  
④ The line $x = 2$ is an axis of symmetry for the graph of the function $f(x)$.

Among these, the correct statements are.

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