
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
The plane $\Pi$ passes through the vertex of a cone, perpendicular to its axis; point $A$ lies in plane $\Pi$. Let $M$ be a point on the cone such that a light ray emanating from $A$ towards $M$, after reflecting off the surface of the cone, becomes parallel to plane $\Pi$. Find the locus of the projections of points $M$ onto plane $\Pi$.

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