
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 \( f(x) \) and \( g(x) \) be an odd function and an even function respectively, both defined on \(\mathbf{R}\). When \( x < 0 \), \( f^{\prime}(x) g(x) + f(x) g^{\prime}(x) > 0 \), and \( g(3) = 0 \). Determine the solution set of the inequality \( f(x) \cdot g(x) < 0 \).

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