
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 point M(3, 2) is at a distance of 4 from the directrix of the parabola $C: y=ax^2$ ($a>0$). Let F be the focus of the parabola, and let N(1, 1). Find the minimum value of $$\frac {|PN|-1}{|PF|}$$ when point P moves along the line $l: x-y=2$.

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