
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
An open-top box has a square base of side $a$ and height $b$. The total surface area including the bottom and the open top of the box, and its volume are numerically equal. If $1 \le a \le b$, find all possible integer pairs $(a, b)$.
**A) $(5, 5)$ only**  
**B) $(4, 4)$ only**  
**C) $(8, 2)$ and $(5, 5)$**  
**D) $(6, 3)$ only**  
**E) None of these**

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