
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
For any three positive integers \( x, y, z \), let
\[ 
f(x, y, z) = [1+2+3+\cdots+(x+y-2)] - z .
\]

Find all positive integer tuples \( (a, b, c, d) \) such that
\[ 
f(a, b, c) = f(c, d, a) = 1993.


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