
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 \( y^2 = 4p(x + p) \) (where \( p > 0 \)), two mutually perpendicular chords \( AB \) and \( CD \) pass through the origin \( O \). Find the minimum value of \( |AB| + |CD| \).

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