
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 $f(x)$ such that $f(x+y) = f(x) + f(x)$, we can deduce that a function formula satisfying this condition is $f(x) = 2x$. Similarly, let $g(x)$ be a function defined on $\mathbb{R}$ satisfying the following properties: (1) $g(x_1 + x_2) = g(x_1) \cdot g(x_2)$, (2) $g(1) = 3$, and (3) for all $x_1 < x_2$, $g(x_1) < g(x_2)$. Write a function expression for $g(x)$ that satisfies the above properties.

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