
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
Given a set \( A = \{0, 1, 2, \cdots, 9\} \), and a family of non-empty subsets \( B_1, B_2, \cdots, B_j \) of \( A \), where for \( i \neq j \), \(\left|B_i \cap B_j\right| \leqslant 2\), determine the maximum value of \( k \).

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