
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 two properties of functions: Property 1: $f(x+2)$ is an even function; Property 2: $f(x)$ is decreasing on $(-\infty, 2)$ and increasing on $(2, +\infty)$. For the functions ①$f(x)=|x+2|$, ②$f(x)=(x-2)^2$, ③$f(x)=\cos(x-2)$, the sequence number(s) of all functions that possess both of the above properties is __________.

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