
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 $M$ be a set consisting of functions $f(x)$ that satisfy the following property: there exists an $x_0$ in the domain such that $f(x_0 + 1) = f(x_0) + f(1)$. Given the following functions: ① $f(x) =$ ; ② $f(x) = 2^x$; ③ $f(x) = \lg(x^2 + 2)$; ④ $f(x) = \cos(\pi x)$. Among these, the functions that belong to set $M$ are __________ (write down the serial numbers of all functions that meet the requirements).

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