
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 $PQR$, angle $P$ is $60^\circ$, and the altitude $PS$ from $P$ to $QR$ measures $2$ centimeters. Calculate the area of triangle $PQR$.

[asy] import olympiad; pair P,Q,R,S; P = (0,2); Q = (sqrt(3),0);
R = (-sqrt(3),0); S = (0,0); draw(P--Q--R--P); draw(P--S,dashed);
label("$60^{\circ}$",P-(0.1,0.5),N); label("$P$",P,N);label("$Q$",Q,E);label("$R$",R,W);label("$S$",S,S);
draw((0,.1)--(.1,.1)--(.1,0)); draw(S + .1*dir(-30)--S + .2*dir(60)--S+.1*dir(150));
[/asy]

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