
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
We know that out of the following four statements concerning the positive integers \( a \) and \( b \), three are true and one is false:

1. \( (a+1) \) is divisible by \( b \);
2. \( a = 2b + 5 \);
3. \( a + b \) is divisible by 3;
4. \( a + 7b \) is a prime number.

Determine the values of \( a \) and \( b \).

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