
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, triangle $ABC$ has sides $AB = 30 \text{ cm}$ and $AC = 24 \text{ cm}$ with $\angle A = 90^\circ$. Adjacent to triangle $ABC$ is triangle $ABD$ where $D$ is on line extended from $B$ and $AD$ also forms a right angle with $AB$. Given $AD = 18 \text{ cm}$, what is the sum of the areas of triangles $ABC$ and $ABD$?

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