
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
For a positive integer \(a\) and integers \(b\), \(c\), the quadratic equation \(a x^{2} + b x + c = 0\) has two roots \(\alpha, \beta\) that satisfy \(0 < \alpha < \beta < 1\). Find the minimum value of \(a\).

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