
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 that \(a\) is a real number, for all real numbers \(x\), the quadratic function \(y = x^2 - 4ax + 2a + 30\) is non-negative. Determine the range of values of the roots of the equation \(\frac{x}{a+3} = |a-1| + 1\).

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