
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 is at \( (-4,2) \). Find the value of \( b - a \).

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