
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
In the diagram below, $BC$ is 12 cm, and $AC$ is 5 cm. The angle between $BC$ and $AC$ is $30^\circ$. In square centimeters, what is the area of triangle $ABC$?

[asy]
import olympiad;
defaultpen(linewidth(0.7));
draw(anglemark((16,0),(23,20),(12,5),20));
draw((0,0)--(16,0)--(23,20)--cycle);
draw((16,0)--(23,0)--(23,20),dashed);
label("12 cm",(8,0),S);
label("5 cm",(23,10),E);
label("$30^\circ$",(19,7),NE);
label("$A$",(23,20),N);
label("$B$",(0,0),SW);
label("$C$",(16,0),SE);
[/asy]

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