
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 $S$ lie in the plane of the square $EFGH$ such that $EFP$, $FGQ$, $GRH$, and $HES$ are equilateral triangles. If the area of square $EFGH$ is 25, find the area of $PQRS$. Express your answer in simplest radical form.

[asy]
pair P,Q,R,S,E,F,G,H;
H=(0,0);
G=(10,0);
F=(10,10);
E=(0,10);
S=(-8.7,5);
Q=(18.7,5);
R=(5,-8.7);
P=(5,18.7);
draw(E--F--G--H--cycle,linewidth(0.7));
draw(E--H--S--cycle,linewidth(0.7));
draw(F--Q--G--cycle,linewidth(0.7));
draw(E--F--P--cycle,linewidth(0.7));
draw(H--G--R--cycle,linewidth(0.7));
draw(P--Q--R--S--cycle,linewidth(0.7));
label("$E$",E,SE);
label("$F$",F,SW);
label("$G$",G,NW);
label("$H$",H,NE);
label("$P$",P,N);
label("$Q$",Q,E);
label("$R$",R,S);
label("$S$",S,W);
[/asy]

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