
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
A set of points \( M \) on the plane and 7 different circles \( C_{1}, C_{2}, \cdots, C_{7} \) satisfy the following condition: the circle \( C_{k} \) contains exactly \( k \) points from \( M \) (for \( k=1, 2, \cdots, 7 \)). What is the minimum number of points in \( M \)?

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