
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
Given \( f(x) \) and \( g(x) \) be odd and even functions defined on \(\mathbf{R}\) respectively, and given \( f^{\prime}(x) \cdot g(x) + f(x) \cdot g^{\prime}(x) > 0 \) when \( x < 0 \), and \( g(-3) = 0 \), find the solution set for the inequality \( f(x) \cdot g(x) < 0 \).

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