
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 \( n \leqslant 2r \), and let \(\mathscr{A} = \{ A_1, A_2, \cdots, A_t \} \) be a family of sets such that \(\left| A_i \right| = r\) for \( i = 1, 2, \cdots, t \). Find the maximum value of \( t \).

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