
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
If altitude $CD$ is $2$ centimeters, what is the number of square centimeters in the area of $\triangle ABC$?

[asy]
import olympiad; 
pair A,B,C,D; 
A = (0,2); 
B = (2,0);
C = (0,0); 
D = midpoint(A--B); 
draw(A--B--C--A); 
draw(C--D,dashed);
label("$45^{\circ}$",A-(0.1,0.1),NW);
label("$A$",A,N); label("$B$",B,E); label("$C$",C,W); label("$D$",D,NE);
[/asy]

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