
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 tournament, Alpha and Charlie both played games worth a total of 600 points. Alpha scored 180 points out of 360 points attempted on the first day, and scored 120 points out of 240 points attempted on the second day. Charlie, who did not attempt 360 points on the first day, had a positive integer score on each of the two days, and Charlie's daily success ratio (points scored divided by points attempted) on each day was less than Alpha's on that day. Alpha's two-day success ratio was $300/600 = 1/2$.

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

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