
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
Alpha and Charlie compete in a four-day coding contest, with each attempting a total of 400 points. Alpha scored 120 points out of 200 points attempted over the first two days, and 80 points out of 200 points attempted over the last two days. Charlie, who did not attempt 200 points on the first two days has a positive integer score on each of the days, with Charlie's daily success ratio (points scored divided by points attempted) lower than Alpha's for those two days and afterwards similiarly. Alpha’s overall success ratio across the four days is $200/400 = 1/2$.

Find the highest possible four-day success ratio that Charlie could achieve.

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