
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 \( x \) and \( y \) is associated with a certain number \( x^{*} y \). Find \( 1993 * 1935 \) if it is known that for any three numbers \( x, y, z \), the following identities hold: 
\[ x^{*} x = 0 \]
\[ x^{*}\left(y^{*} z\right) = \left(x^{*} y\right) + z \]

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