
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 chess competition, Gamma and Delta each played matches with potential total points of 600. Gamma scored 180 points out of 360 points on the first day, and 150 points out of 240 points on the second day. Delta, who did not attempt 360 points on the first day, scored a positive integer number of points each day, and Delta's daily success ratio (points scored divided by points attempted) on each day was less than Gamma's on that day. Gamma's two-day success ratio was $330/600 = 11/20$.

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

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