
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
In a two-day problem-solving contest, both Alpha and Beta participated, each attempting questions worth a total of 600 points. Alpha scored 192 points out of 360 points attempted on the first day, and 168 points out of 240 points attempted on the second day. Beta, who did not attempt 360 points on the first day and 240 on the second, had a positive integer score on each day, and Beta’s daily success ratio (points scored divided by points attempted) on each day was less than Alpha's on that day. Additionally, Beta's total points attempted over the two days were not more than 550.

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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