
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
Two right triangles share a side such that one side of both triangles is incorporated into the side lengths and vertices as shown:

[asy]
pair pA, pB, pC, pD;
pA = (0, 0);
pB = pA + 8 * dir(0);
pC = pA + 12 * dir(90);
pD = pB + 8 * dir(90);
label("$A$", pA, SW);
label("$B$", pB, SE);
label("$C$", pC, NW);
label("$D$", pD, NE);
label("$8\ \text{units}$", pA--pB, S);
label("$12\ \text{units}$", pA--pC, W);
label("$8\ \text{units}$", pB--pD, E);
draw(pA--pB--pC--pA);
draw(pB--pD--pA);
draw(rightanglemark(pB,pA,pC,15));
draw(rightanglemark(pD,pB,pA,15));
[/asy]

Find the area of $\triangle ACD$. Assume $AD$ bisects $\angle CAB$.

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