
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
Let function $g(x)$ satisfy $g(1) = 1$ and
\[g(x + y) = 2^y g(x) + 3^x g(y)\] for all real numbers $x$ and $y$. Find the function $g(x)$.

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