
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 a square $ABCD$ with vertices $A(1,1), B(-1,1), C(-1,-1), D(1,-1)$, find the matrix $\mathbf{N}$ that performs the transformation which sends this square to a new square $A'B'C'D'$ such that the transformation involves a 30-degree rotation followed by scaling by a factor of 2.

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