
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 circles with centers $O_{1}$ and $O_{2}$ intersect at points $A$ and $C$. Draw a secant $B_{1} B_{2}$ through point $A$. What is the locus of the intersection point $M$ of the lines $B_{1} O_{1}$ and $B_{2} O_{2}$?

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