
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 \( A \) be the fixed point \((b, 0)\), \( P \) be a point on the circle \( x^2 + y^2 = 9 \), and \( M \) be a point on \( AP \) such that \(\frac{AM}{MP} = \frac{1}{2} \). Find the equation of the locus of point \( M \) as point \( P \) moves on the circle.

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