
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
The two numbers representing Jack's and Bill's ages are formed by the same digits but in different roles. Jack's age is given by \(10a + b\) where \(a\) and \(b\) are digits, and Bill's age is \(b^2 + a\). In six years, Jack's age will be three times what Bill's age will be. Find the difference in their ages now.
A) 9
B) 18
C) 19
D) 20
E) 25

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