
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 \( A_1, A_2, \ldots, A_m \) be finite sets of size 2012 and let \( B_1, B_2, \ldots, B_m \) be finite sets of size 2013 such that \( A_i \cap B_j = \emptyset \) if and only if \( i = j \). Find the maximum value of \( m \).

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