
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 a function $f(x)$ that satisfies: for any real numbers $x_1$, $x_2$. When $x_1 < x_2$, we have $f(x_1) < f(x_2)$, and $f(x_1+x_2) = f(x_1)f(x_2)$. Write a function that meets the above conditions.

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