
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
The number \(2002\) is expressed as \(2002 = \frac{a_1!a_2!...a_m!}{b_1!b_2!...b_n!}\), where \(a_1 \ge a_2 \ge ... \ge a_m\) and \(b_1 \ge b_2 \ge ... \ge b_n\) are positive integers and \(a_1 + b_1\) is minimized. What is \(|a_1 - b_1|\)?
A) \(0\)  
B) \(1\)  
C) \(2\)  
D) \(3\)  
E) \(4\)

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