
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
To each pair of numbers \(x\) and \(y\), a certain number \(x * y\) is assigned. Find \(1993 * 1935\), given that for any three numbers \(x, y\), and \(z\), the following identities hold: \(x * x = 0\) and \(x * (y * z) = (x * y) + z\).

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