
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
In the plane Cartesian coordinate system \( xOy \), curve \( C_1: y^2 = 4x \), and curve \( C_2: (x-4)^2 + y^2 = 8 \), draw a line \( l \) through a point \( P \) on curve \( C_1 \) with an inclination angle of \(45^\circ\), which intersects curve \( C_2 \) at two distinct points \( Q \) and \( R \). Find the range of values for \( |PQ||PR| \).

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