
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
Angle $PMC$ is a right angle, with $PM=12$ units. Compute the total area of the equilateral triangle $PQR$ and square $PMCD$.

[asy]
draw((0,0)--(1,1)--(2,0)--(1,-1)--cycle);
draw((1,1)--(1,2)--(3,3)--(3,2)--cycle);
draw((1,1)--(3,2));

label("P", (1,1), SE);
label("M", (1,-1), S);
label("C", (0,0), S);
label("D", (2,0), S);
label("Q", (1,2), N);
label("R", (3,3), N);
label("12", (1.5, 0), SE);
[/asy]

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