
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
Gamma and Delta both participated in a two-day science quiz. Each attempted questions totaling 600 points after the second day. On the first day, Gamma scored 210 points out of 350 points attempted, and on the second day scored 150 points out of 250 points attempted. Delta, who also did not attempt 350 points on the first day, scored a positive integer number of points on each of the two days, 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 overall success ratio for the two days was $360/600 = 3/5$.

Find the largest possible overall success ratio that Delta could have achieved.

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