
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
Alpha and Beta both took part in a three-day problem-solving competition. At the end of the third day, each had attempted questions worth a total of 600 points. Alpha scored 200 points out of 300 points attempted on the first day, and 150 points out of 200 on the second day, then 100 points out of 100 on the third day. Beta, who did not attempt 300 points on the first day and 200 on the second day, had a positive integer score on each of the three days. Furthermore, Beta's daily success ratio on each day was less than Alpha's on that day. Alpha's three-day success ratio was \( \frac{450}{600} = 0.75 \).

Find the largest possible three-day success ratio that Beta could have achieved.

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