
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 \(y^{2} = 2px \) (where \( p > 0 \)) and a variable chord \( AB \) of length \( l \), find the shortest distance from the midpoint \( M \) of chord \( AB \) to the \( y \)-axis, and determine the coordinates of this point \( M \).

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