
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
What is the greatest number of points of intersection that can occur when $2$ different circles and $3$ different straight lines are drawn on the same piece of paper, assuming the third line intersects only one of the circles and not the other line or circle?

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