
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 all pairs of natural numbers \( a \) and \( b \) for which three of the following four statements are true, and one is false:

1) \( a^{2}+6a+8 \) is divisible by \( b \);
2) \( a^{2}+ab-6b^{2}-15b-9=0 \);
3) \( a+2b+2 \) is divisible by 4;
4) \( a+6b+2 \) is a prime number.

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