
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 a triangle, the points $B$, $D$, and $C$ lie on a straight line with $D$ between $B$ and $C$. The ratio of $BD$ to $DC$ is $3$ to $2$. The area of $\triangle ABD$ is $30$ square centimeters. What is the area of $\triangle ADC$? Assume both triangles share the same height from vertex $A$ perpendicular to line $BC$.

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