
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 $ABC$ is a right triangle at $A$ with $AB = 15\text{ cm}$ and $AC = 10\text{ cm}$. There is another right triangle $ABD$, right at $B$, sharing side $AB$ with $ABC$, and the length of $BD$ is $8\text{ cm}$. Calculate the total area of the triangles $ABC$ and $ABD$.

[asy]
draw((0,0)--(15,0)--(0,10)--cycle,black+linewidth(1));
draw((15,0)--(15,8)--(0,10)--cycle,black+linewidth(1));
draw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black+linewidth(1));
label("$A$",(0,0),SW);
label("$B$",(15,0),SE);
label("$C$",(0,10),NW);
label("$D$",(15,8),NE);
[/asy]

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