
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
Let $P$ be a moving point on the parabola $y^2 = 2x$. A tangent line is drawn at $P$ to the parabola, which intersects the circle $x^2 + y^2 = 1$ at points $M$ and $N$. The tangents to the circle at points $M$ and $N$ intersect at point $Q$. Find the equation of the locus of point $Q$.

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