
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
If $f(x)$ satisfies $f(x+y)=f(x)+f(y)$, then one can write a function that satisfies this condition as $f(x)=2x$. By analogy, if a function $g(x)$ defined on $\mathbb{R}$ satisfies: (1) $g(x_1+x_2)=g(x_1) \cdot g(x_2)$; (2) $g(1)=3$; (3) $\forall x_1 < x_2$, $g(x_1) < g(x_2)$, then one can write a function that satisfies the above properties as .

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