
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
In triangle $PQR$, the altitude $PS$ is $2$ centimeters, and $\angle PRQ = 60^{\circ}$. What is the number of square centimeters in the area of $\Delta PQR$?

[asy] 
import olympiad; 
pair P,Q,R,S; 
P = (0,2); Q = (-1,0);
R = (1,0); 
S = (0,0); 
draw(P--Q--R--P); 
draw(P--S,dashed);
label("$60^{\circ}$",P-(0.05,0.3),E);
label("$P$",P,N);label("$Q$",Q,W);label("$R$",R,E);label("$S$",S,S);
draw((0,.1)--(.1,.1)--(.1,0)); 
draw(S + .1*dir(210)--S + sqrt(2)*.1*dir(165)--S+.1*dir(120));
[/asy]

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