
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
There is a smallest positive real number \(a\) such that there exists a positive real number \(b\) such that all the roots of the polynomial \(x^3 - ax^2 + bx - a^2\) are real. For this value of \(a\), the value of \(b\) is unique. What is the value of \(b\)?

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