
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 function $f(x)$ defined on $(-\infty, +\infty)$ is an even function and satisfies $f(x+1) = -f(x)$. Also, $f(x)$ is increasing on the interval $[-1, 0]$. Among the following five statements about $f(x)$: 
1. $f(x)$ is a periodic function.
2. The graph of $f(x)$ is symmetric about $x=1$.
3. $f(x)$ is increasing on the interval $[0, 1]$.
4. $f(x)$ is decreasing on the interval $[1, 2]$.
5. $f(2) = f(0)$.

The true statements are. (Write down the numbers of all true statements)

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