
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
A solid right prism $PQRSUV$ has a height of 18, as shown. Also, its bases are equilateral triangles with side length 10. Points $M$, $N$, and $O$ are the midpoints of edges $PQ$, $QR$, and $PR$, respectively. Determine the perimeter of triangle $MNO$. [asy]
pair P, Q, R, S, U, V, M, N, O;
P=(0,0);
Q=(10,0);
R=(5,-5);
S=(5,-23);
U=(0,-18);
V=(10,-18);
M=(P+Q)/2;
N=(Q+R)/2;
O=(R+P)/2;
draw(P--Q--R--P--U--S--V--Q--R--S);
draw(M--N--O--M, dashed);
label("$P$", P, NW);
label("$Q$", Q, NE);
label("$R$", R, N);
label("$S$", S, S);
label("$U$", U, SW);
label("$V$", V, SE);
label("$M$", M, SW);
label("$N$", N, SE);
label("$O$", O, SE);
label("10", (P+Q)/2, dir(90));
label("18", (P+V)/2, dir(0));
[/asy]

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