
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
Find the area of triangle $JKL$, where $\angle K = 45^\circ$ and $(KL) = 20$.

[asy]
unitsize(1inch);
pair P,Q,R;
P = (0,0);
Q= (sqrt(2),0);
R = (0,sqrt(2));
draw (P--Q--R--P,linewidth(0.9));
draw(rightanglemark(Q,P,R,3));
label("$J$",P,S);
label("$K$",Q,S);
label("$L$",R,N);
label("$20$",(Q+R)/2,NE);
label("$45^\circ$",(0,0.75),E);
[/asy]

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