
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 a decreasing function on $(-\infty, 2)$ and an increasing function on $(2, +\infty)$. For the functions ① $f(x) = |x+2|$, ② $f(x) = (x-2)^2$, ③ $f(x) = \cos(x-2)$, identify all functions that possess both of the given properties.

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