
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 competition, Alpha and Gamma both attempted a total of 500 points. On the first day, Alpha scored 170 points out of 280 points attempted, and on the second day, he scored 150 points out of 220 points attempted. Gamma attempted fewer points than Alpha on the first day and managed to score a positive integer number of points on each day. Gamma's daily success ratio (points scored divided by points attempted) was less than Alpha's on both days. Alpha's overall success ratio was $320/500 = 0.64$.

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

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