
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
Determine the natural integers $(a, b)$ greater than or equal to 3 such that: $ab^{2} + b + 7 \mid a^{2}b + a + b$.

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