
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
Five pairs of twin siblings participate in $k$ groups of activities. The conditions are:
1. Twin siblings are not in the same group.
2. Any two people who are not twin siblings have participated in exactly one group together.
3. One person participates in only two groups.

What is the minimum value of $k$?

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