
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 the center of the circle \((x+1)^{2}+y^{2}=100\) be \(C\), and \(A(1,0)\) be a fixed point inside the circle. Let \(Q\) be any point on the circumference of the circle. The perpendicular bisector of segment \(AQ\) intersects the line connecting \(C\) and \(Q\) at point \(M\). Determine the equation of the trajectory of \(M\).

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