
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
Given that the frequencies of the first 4 groups form a geometric sequence, the frequencies of the last 6 groups form an arithmetic sequence, and there are 200 senior high school students in total, determine the maximum number of students in one group and the frequency of vision between 4.6 to 5.0.

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