
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
Find all real number sequences \(\{b_{n}\}\) and \(\{c_{n}\}\) (for \(n \geq 1\)) that satisfy the following two conditions:
1. For any positive integer \(n\), \(b_{n} \leq c_{n}\).
2. For any positive integer \(n\), \(b_{n+1}\) and \(c_{n+1}\) are the roots of the quadratic equation \(x^{2} + b_{n} x + c_{n} = 0\).

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