
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 the function \( f(x)=x^2+ax \ (a\in \mathbb{R}) \), let \( g(x)= \begin{cases} f(x), & x \geq 0, \\ f'(x), & x < 0, \end{cases} \) where \( f'(x) \) is the derivative of \( f(x) \). If the equation \( g(f(x))=0 \) has four distinct real roots, determine the range of values for \( a \).

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