
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
Vera has a set of weights, each of which has a distinct mass and weighs an integer number of grams. It is known that the lightest weight in the set weighs 71 times less than the sum of the weights of all other weights in the set. It is also known that the two lightest weights together weigh 34 times less than the sum of the weights of all other weights in the set. What is the minimum number of grams the lightest weight can weigh?

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