
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 the function $f(x) = |x^2 - 2mx + n|, x \in \mathbb{R}$, consider the following conclusions:  
① The function $f(x)$ is an even function;  
② If $f(0) = f(2)$, then the graph of the function $f(x)$ must be symmetric about the line $x = 1$;  
③ If $m^2 - n \leq 0$, then the function $f(x)$ is decreasing on the interval $(-\infty, m]$;  
④ The function $f(x)$ has a minimum value of $|n - m^2|$. The correct conclusions are marked with their index numbers.

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