
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 took part in a two-day problem-solving challenge, both attempting questions equally worth a total of 500 points. On the first day, Alpha scored 200 points out of 300 points attempted. On the second day, Alpha scored the remaining 100 points from 200 points attempted. Beta, attempting fewer points than Alpha on both days with a non-zero integer score, must have lower daily success ratios than Alpha each day, with Alpha's overall success ratio for the two days being $\frac{300}{500} = 0.6$.

Find the highest possible two-day success ratio Beta could have achieved, assuming Beta attempted exactly 220 points on the first day.

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