
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
An \((l, a)\)-design of a set is a collection of subsets of that set such that each subset contains exactly \(l\) elements and that no two of the subsets share more than \(a\) elements. How many \((2,1)\)-designs are there of a set containing 8 elements?

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