
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
The product of the four numbers that are the roots of the equations \( x^{2} + 2bx + c = 0 \) and \( x^{2} + 2cx + b = 0 \) is equal to 1. It is known that the numbers \( b \) and \( c \) are positive. Find them.

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