
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
Each pair of numbers \(A\) and \(B\) is assigned a certain number \(A * B\). Find \(2021 * 1999\), given that for any three numbers \(A\), \(B\), and \(C\), the following identities are satisfied: \(A * A = 0\) and \(A * (B * C) = (A * B) + C\).

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