
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 rectangular coordinate system \(xOy\), there are two curves \(C_{1}: y^{2}=4x\) and \(C_{2}:(x-4)^{2}+y^{2}=8\). From a point \(P\) on \(C_{1}\), a line \(l\) with an angle of inclination of \(45^\circ\) is drawn, intersecting \(C_{2}\) at two distinct points \(Q\) and \(R\). Find the range of the values of \( |PQ| \cdot |PR| \).

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