
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
The domain of the function $f(x)$ is $A$. If $x_1, x_2 \in A$, and $f(x_1) = f(x_2)$ always implies $x_1 = x_2$, then $f(x)$ is called an injective function. For example, $f(x) = 2x + 1$ ($x \in \mathbb{R}$) is an injective function. Consider the following statements:  
① The function $f(x) = x^2$ ($x \in \mathbb{R}$) is an injective function;  
② The function $f(x) = 2^x$ ($x \in \mathbb{R}$) is an injective function;  
③ If $f(x)$ is an injective function, and $x_1, x_2 \in A$ with $x_1 \neq x_2$, then $f(x_1) \neq f(x_2)$;  
④ A function that is monotonic on its domain is always an injective function.  
Among these statements, the true ones are (write down the numbers of all true statements).

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