
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
Consider the set of all equations of the form \(x^3 + bx^2 + cx + d = 0\), where \(b\), \(c\), \(d\) are real constants and \(|b| \leq 1\), \(|c| \leq 1.5\), \(|d| \leq 1\). Determine the range of the largest positive real number \(s\) which satisfies at least one of these equations.

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