
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 Gamma both took part in a two-day work-efficiency study. At the end of the second day, each had completed tasks worth a total of 600 points. Alpha managed 180 points out of 360 points attempted on the first day, and scored 150 points out of 240 points attempted on the second day. Gamma, who did not attempt as many points as Alpha 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 $\frac{330}{600} = \frac{11}{20}$.

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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