
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 $\mathbb{R}$ that is not a constant function and satisfies $f(x-1) = f(x+1)$ and $f(2-x) = f(x)$ for all $x \in \mathbb{R}$. There are 5 conclusions drawn about this function:
① $f(x)$ is an even function,
② The graph of $f(x)$ is symmetric about $x=1$,
③ $f(x)$ is a periodic function,
④ $f(x)$ is a monotonic function,
⑤ $f(x)$ has maximum and minimum values.
Identify the correct statements.

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