
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
Which of the following theorems are true?
1) If each term is divisible by 7, then the sum is divisible by 7.
2) If each term is not divisible by 7, then the sum is not divisible by 7.
3) If at least one term is divisible by 7, then the sum is divisible by 7.
4) If the sum is divisible by 7, then each term is divisible by 7.
5) If the sum is not divisible by 7, then each term is not divisible by 7.
6) If the sum is not divisible by 7, then at least one term is not divisible by 7.

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