
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 \( Q(c,d) \) in the \( xy \)-plane is first rotated counterclockwise by \( 90^\circ \) around the point \( (3,2) \) and then reflected about the line \( y = x \). The image of \( Q \) after these transformations is at \( (1,-4) \). What is \( d - c \)?
**A)** \(-11\)
**B)** \(-9\)
**C)** \(-7\)
**D)** \(-5\)
**E)** \(-3\)

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