
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
Let \(2 \leq r < \frac{n}{2}\). Given \(A = \{A_{1}, A_{2}, \cdots, A_{t}\}\) as a family of sets, where \(\left|A_{i}\right|=r\) for \(i=1,2, \cdots, t\), find the maximum value of \(t\).

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