
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 tournament, Alpha and Gamma both attempted questions worth a total of 600 points. Alpha scored 210 points out of 350 points on the first day, and 150 points out of 250 points on the second day. Gamma, who did not attempt 350 points on the first day, had a positive integer score on each of the two days, and Gamma'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 $\frac{360}{600} = 3/5$.

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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