
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 any \( x_1, x_2 \) \((x_1 \neq x_2)\) in the domain of the function \( f(x) \), the following statements hold:
(1) \( f(x_1 + x_2) = f(x_1) \cdot f(x_2) \)
(2) \( f(x_1 \cdot x_2) = f(x_1) + f(x_2) \)
(3) \( \frac{f(x_1) - f(x_2)}{x_1 - x_2} > 0 \)
(4) \( f\left(\frac{x_1 + x_2}{2}\right) > \frac{f(x_1) + f(x_2)}{2} \)

When \( f(x) = 10^x \), the correct statements are: ______

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