
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
What is the matrix $\mathbf{N}$ that performs the transformation which sends square $PQRS$ with vertices $P(1, 1), Q(1, 2), R(2, 2), S(2, 1)$ to a new square $P'Q'R'S'$ such that $P$ maps to $P'$, $Q$ to $Q'$, and so on? The transformation involves a $90^\circ$ clockwise rotation followed by a scaling of factor 2.

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