
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
A rectangular room measures $a$ by $b$ feet where $a$ and $b$ are positive integers, with $b > a$. A painter wants to paint a rectangular area on the floor such that the sides of the painted area are parallel to the sides of the room, and the unpainted part around the painted rectangle forms a border that is consistently 2 feet wide around the painted rectangle. The unpainted border occupies four times the area of the painted rectangle. Find all possible values for $a$ and $b$.
- **A**: (6, 30)
- **B**: (10, 10)
- **C**: (5, 25)
- **D**: (7, 35)
- **E**: None of the above

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