
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
Tangents are drawn from a point \( P \) on the plane to the parabola \( y^2 = 2px \). The slopes of these tangents, \( m_1 \) and \( m_2 \), satisfy the equation

$$
m_1 m_2^2 + m_1^2 m_2 = k,
$$

where \( k \) is a given constant. What is the locus of the point \( P \)?

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