
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 $(2,4)$ and then reflected about the line $y = -x$. The image of $P$ after these two transformations is located at $(-4,2)$. What is $b - a$?
A) 8  
B) 9  
C) 10  
D) 11  
E) 12

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