
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
How many sets of integers \( (a, b, c, d) \) satisfy:
\[ 0 < a < b < c < d < 500, \]
\[ a + d = b + c, \]
and
\[ bc - ad = 93? \]
(The 11th USA Mathematical Talent Search, 1993)

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