
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
We have selected 7 subsets of a finite set, each containing 3 elements, such that any two distinct elements are contained in exactly one of the selected subsets.

a) How many elements does the set have?

b) What is the maximum number of selected subsets that can be chosen such that no three of them contain the same element?

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