
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
Students A and B each took out 4 books as prizes for a dice game. They agreed that if the number of dots on the top face of the dice is odd, student A gets 1 point; otherwise, student B gets 1 point. The first to accumulate 3 points wins all 8 books and ends the game. After the game started, student A scored 2 points, and student B scored 1 point. Determine the reasonable distribution of the 8 books.

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