
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 $\mathbf{M}$ that performs the transformation which sends square $ABCD$ to square $A'B'C'D'$, where $A$ goes to $A'$, $B$ goes to $B'$, $C$ goes to $C'$, and $D$ goes to $D'$? Specifically, $ABCD$ is rotated by $30^\circ$ clockwise and scaled by a factor of 2.

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