
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
Alice and Bob both participated in a two-day contest. At the end of both days, each had attempted problems worth a total of 600 points. Alice scored 220 points out of 400 points attempted on the first day and scored 180 points out of 200 points attempted on the second day. Bob, who did not attempt 400 points on the first day and did not attempt 200 points on the second day, had a positive integer score each day, and his success ratio (points scored divided by points attempted) each day was less than Alice's on that day. Alice's two-day success ratio was $\frac{2}{3}$.

Find Bob's highest possible two-day success ratio.

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