
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
Given that P(x<sub>1</sub>, y<sub>1</sub>) and Q(x<sub>2</sub>, y<sub>2</sub>) are two distinct points on the curve $$y = 2\sqrt{x}$$, and F(1, 0) with x<sub>2</sub> = 3x<sub>1</sub> + 2, find the value of $$\frac{|QF|}{|PF|}$$.

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