
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
Find the natural numbers \( a \) and \( b \) if out of the four statements below:
1) \( a - b \) is divisible by 3,
2) \( a + 2b \) is a prime number,
3) \( a = 4b - 1 \),
4) \( a + 7 \) is divisible by \( b \),

three are true and one is false. Find all solutions.

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