
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
$PQRSTU$ is a cube with a volume of 8. Find the volume of the pyramid $PQRS$.

[asy]
import three;
triple P,Q,R,S,T,U,V,W;
P = (0,0,0);
Q = (2,0,0);
R = (2,2,0);
S = (0,2,0);
T = (0,0,2);
U = Q+T;
V = R + T;
W = S + T;
draw(Q--R--S);
draw(Q--P--S,dashed);
draw(T--U--V--W--T);
draw(P--T,dashed);
draw(Q--U);
draw(R--V);
draw(S--W);
label("$P$",P,S);
label("$Q$",Q,W);
label("$R$",R,S);
label("$S$",S,E);
label("$T$",T,N);
label("$U$",U,W);
label("$V$",V,NW);
label("$W$",W,E);
[/asy]

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