
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
Given triangle $PQR$ with vertices $P(1, 1)$, $Q(2, 2)$, and $R(2, 1)$, what matrix $\mathbf{N}$ represents the transformation which sends triangle $PQR$ to triangle $P'Q'R'$, such that the transformation includes a reflection across the line $y = x$ combined with a scaling of factor 2?

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