
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:
1. For any $x_1, x_2 \in \mathbb{R}$, we have $f(x_1 + x_2) = f(x_1) \cdot f(x_2)$;
2. For any $x_1, x_2 \in \mathbb{R}$, when $x_1 < x_2$, we have $f(x_1) < f(x_2)$.

Please write a function that satisfies both of the above conditions.

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