
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
For the function $f(x)$ defined within its domain for any $x_1$, $x_2$ ($x_1 \neq x_2$),

1. $f(x_1 + x_2) = f(x_1)f(x_2)$;
2. $f(x_1 \cdot x_2) = f(x_1) + f(x_2)$;
3. $f(x) > 0$;
4. $f'(x) > 0$.

When $f(x) = 2^x$, the correct statements among the above are \_\_\_\_\_\_.

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