
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 participated in a two-day problem-solving competition. At the end of the second day, each had attempted questions worth a total of 700 points. Alpha scored 210 points out of 400 points attempted on the first day, and scored 210 points out of 300 points attempted on the second day. Beta, who did not attempt 400 points on any day, had a positive integer score on each of the two days, and Beta's daily success ratio (points scored divided by points attempted) on each day was less than Alpha's on that day. Alpha's two-day success ratio was $420/700 = 3/5$.

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

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