
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
Al, Bert, Carl, and Dan are the winners of a school contest for a pile of books, which they are to divide in a ratio of $4:3:2:1$, respectively. Due to some confusion, they come at different times to claim their prizes, and each assumes he is the first to arrive. If each takes what he believes to be his correct share of books, what fraction of the books goes unclaimed?
A) $\frac{189}{2500}$
B) $\frac{21}{250}$
C) $\frac{1701}{2500}$
D) $\frac{9}{50}$
E) $\frac{1}{5}$

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