
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 plane $\alpha$ with the Cartesian coordinate system $xOy$, there are two sets, $A=\{P|P \text{ is a point on a circle in } \alpha\}$, $B=\{Q|Q \text{ is a point on a certain line in } \alpha\}$. Determine the maximum possible number of elements in the intersection of sets $A$ and $B$.

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