
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 Cartesian coordinate system $xOy$, curve $C_{1}: y^{2}=4x$ and curve $C_{2}:(x-4)^{2}+y^{2}=8$. A line $l$ with a slope of $45^\circ$ passes through a point $P$ on $C_{1}$ and intersects $C_{2}$ at two distinct points $Q$ and $R$. Find the range of values for $|PQ| \cdot |PR|$.

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