
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 four numbers \(1, a, b, c\) that satisfy \(1 < a < b < c\) and such that the sums of every pair of these numbers are all distinct, these 6 sums form an arithmetic sequence from smallest to largest with a total sum of 201. Find the values of \(a, b, c\).

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