
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
Points $P$, $Q$, $R$, and $S$ are placed in the plane so that $APB$, $BQC$, $CRD$, and $DSA$ form equilateral triangles outside a regular pentagon $ABCDE$ where each side is 2 units. Find the area of $PQRS$. 

[asy]
pair P, Q, R, S, A, B, C, D, E;
A=(-20,0);
B=(0,20);
C=(20,20);
D=(40,0);
E=(20,-20);
P=rotate(60,A)*B;
Q=rotate(60,B)*C;
R=rotate(60,C)*D;
S=rotate(60,D)*E;
draw(A--B--C--D--E--cycle,linewidth(0.7));
draw(A--P--B--Q--C--R--D--S--E--cycle,linewidth(0.7));
label("$A$",A,W);
label("$B$",B,N);
label("$C$",C,N);
label("$D$",D,E);
label("$E$",E,S);
label("$P$",P,NW);
label("$Q$",Q,NE);
label("$R$",R,NE);
label("$S$",S,SE);
// Dashline for quadrilateral PQRS
draw(P--Q--R--S--cycle,linetype("4 4"));
[/asy]

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