
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 circle F: (x-1)²+y²=1, moving point Q(x, y) (x≥0), line segment QF intersects circle F at point P, and the length of line segment PQ is equal to the distance from point Q to the y-axis.
1. Find the equation of the trajectory W of moving point Q.
2. Line l passing through point F intersects curve W at points A and D, and intersects circle F at points B and C, where B is on line segment AF and C is on line segment DF. Find the minimum value of |AB|+4|CD| and the slope of line l at this time.

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