
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
Suppose the function $g(x)$ satisfies the equation
\[g(x+y) = g(x)g(y)\]
for all real numbers $x$ and $y$, and $g(0) \neq 0$. Additionally, it is known that $g(1) = 2$. Find $g(3)$.

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