
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, both Charlie and Delta attempted questions worth a total of 600 points. Charlie scored 210 points out of 400 points attempted on the first day, and scored 150 points out of 200 points attempted on the second day. Delta, attempting a different number of points from Charlie on the first day, achieved a positive integer score on each day. Additionally, Delta's daily success ratio (points scored divided by points attempted) on each day was less than Charlie's on that day. Charlie's two-day success ratio was $(210 + 150)/600 = 3/5$.

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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