
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
In the Cartesian plane, given three points \( M(0,0) \), \( P(0,5) \), \( Q\left(\frac{12}{5}, \frac{9}{5}\right) \), let \( A \) be the set of circles passing through point \( M \), \( B \) be the set of circles passing through point \( P \), and \( C \) be the set of circles passing through point \( Q \). Determine the equation of the curve represented by the point set \( A \cap B \cap C \).

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