
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
On the sides of the triangle $ABC$, squares $ABMN$, $BCKL$, and $ACPQ$ are constructed outward. On the segments $NQ$ and $PK$, squares $NQZT$ and $PKXY$ are constructed. The difference in areas of squares $ABMN$ and $BCKL$ is $d$. Find the difference in areas of squares $NQZT$ and $PKXY$:

a) in the case where angle $ABC$ is a right angle,

b) in the general case.

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