
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 point $P(a,b)$ in the $xy$-plane is first rotated counterclockwise by $90^\circ$ around the point $(2,3)$ and then reflected about the line $y=x$. The image of $P$ after these two transformations ends up at the position $(4,1)$. What is $b - a$?
- **A) 1**
- **B) 2**
- **C) -1**
- **D) 3**

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