
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 quadratic curve represented by the equation \( y = mx^2 + k \), and a point \( P(a, b) \) off the curve, find the shortest distance from \( P \) to the curve.

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