
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
On a plane, two non-overlapping circles are given. Is it necessary that there exists a point $M$ lying outside these circles, satisfying the following condition: every line passing through point $M$ intersects at least one of these circles?

Find the locus of points $M$ that satisfy this condition.

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