
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 an even function $f(x)$ defined on $\mathbb{R}$ that satisfies $f(x + 4) = f(x) + f(2)$, and the function $y = f(x)$ is monotonically decreasing on the interval $[0, 2]$. Consider the following four statements:  
① $f(2) = 0$;  
② $x = -4$ is a line of symmetry for the graph of $y = f(x)$;  
③ The function $y = f(x)$ is monotonically increasing on the interval $[8, 10]$;  
④ If the equation $f(x) = m$ has two roots $x_1$ and $x_2$ in the interval $[-6, -2]$, then $x_1 + x_2 = -8$.  

Which of the above statements are correct?

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