
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 line \( y = mx + b \) (where \( |m| < 1 \) and \( |b| < 1 \)) intersects the circle \( x^2 + y^2 = 1 \) at points \( P \) and \( Q \), and intersects the hyperbola \( x^2 - y^2 = 1 \) at points \( R \) and \( S \). Given that points \( P \) and \( Q \) divide the line segment \( RS \) into three equal parts, find the values of \( m \) and \( b \).

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