
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 line l: y = 2x + b is intercepted by the parabola C: y² = 2px (p > 0) with a chord length of 5. The line l passes through the focus of the parabola C. Point M is a moving point on C, and point N has coordinates (3, 0). Find the minimum value of MN.

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