
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
Consider a point $Q(a,b)$ in the $xy$-plane. The point is first mirrored across the line $y = x$ and then rotated by $180^\circ$ around the point $(1,5)$. If the image of $Q$ after these transformations is at $(-8,2)$, determine the value of $a - b$.
A) -4
B) -2
C) 0
D) 2
E) 4

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