
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 transformations is at \( (5, 1) \). What is \( b - a \)?
A) -1
B) 0
C) 1
D) 2
E) 3

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