
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
Express the number 3121 as \( \frac {a_1!a_2! \cdots a_m!}{b_1!b_2! \cdots b_n!} \), where \( a_1 \ge a_2 \ge \cdots \ge a_m \) and \( b_1 \ge b_2 \ge \cdots \ge b_n \) are positive integers and \( a_1 + b_1 \) is as small as possible. Determine \( |a_1 - b_1| \).
A) 1
B) 2
C) 3
D) 4

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