
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 a rule that assigns a number \( x^{*} y \) to each pair of numbers \( x, y \), such that for any \( x \), \( y \), and \( z \) the following identities hold:

1) \( x^{*} x = 0 \)
2) \( x^{*}(y^{*} z) = (x^{*} y) + z \).

Find \( 1993 * 1932 \).

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