
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 $PQRSTU$ has a height of 20 units and its bases are equilateral triangles with a side length of 10 units. Points $J$, $K$, and $L$ are respectively the midpoints of edges $PQ$, $QR$, and $PT$. Determine the perimeter of triangle $JKL$. [asy]
pair P, Q, R, S, T, U, J, K, L;
P=(0,0);
Q=(10,0);
R=(5,-5*sqrt(3));
S=(5,-25);
T=(0,-20);
U=(10,-20);
J=(P+Q)/2;
K=(Q+R)/2;
L=(P+T)/2;
draw(P--Q--R--P--T--U--S--Q--R--T);
draw(J--K--L--J, dashed);
label("$P$", P, NW);
label("$Q$", Q, NE);
label("$R$", R, N);
label("$S$", S, S);
label("$T$", T, SW);
label("$U$", U, SE);
label("$J$", J, NW);
label("$K$", K, NE);
label("$L$", L, SW);
label("10", (P+Q)/2, dir(90));
label("20", (P+T)/2, dir(0));
[/asy]

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