
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 the parabola C: y²=2x with a focus at point F, two lines l₁ and l₂ are drawn passing through point F. Line l₁ intersects parabola C at points A and B, and line l₂ intersects parabola C at points D and E. If the sum of the squares of the slopes of l₁ and l₂ is 2, find the minimum value of |AB|+|DE|.

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