
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 \( g(x) : \mathbb{R} \to \mathbb{R} \) be a function such that
\[
\frac{g(x) g(y) - g(xy)}{5} = 2x + 2y + 8
\]
for all \( x, y \in \mathbb{R} \). Find \( g(x) \).

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