
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 the set \( A = \{0, 1, 2, \cdots, 9\} \), and a collection of non-empty subsets \( B_1, B_2, \cdots, B_k \) of \( A \) such that for \( i \neq j \), \( B_i \cap B_j \) has at most two elements, determine the maximum value of \( k \).

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