
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 math competition, Charlie and Delta both attempted a total of 600 points. Charlie scored 200 points out of 400 attempted on the first day, and 160 points out of 200 attempted on the second day. Delta, who did not attempt 400 points on the first day, scored a positive integer number of points each day, and Delta's daily success ratio was less than Charlie's on each day. Charlie's two-day success ratio was $\frac{360}{600} = \frac{3}{5}$.

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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