
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 F is the focus of the parabola C: x²=4y, the line l passing through point F intersects with parabola C at two distinct points A and B. The tangents to the parabola C at points A and B are l₁ and l₂, respectively, which intersect at point P. Find the minimum value of |PF| + $\frac {32}{|AB|}$.

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