
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, \(AB = 40 \mbox{ cm}\), \(AC = 30 \mbox{ cm}\), and \(\angle A = 90^\circ\). Triangle \(ABC\) has its right angle at \(A\), and point \(D\) is the midpoint of \(AB\). Calculate both the area of triangle \(ABC\) and the length of \(AD\).

[asy]
draw((0,0)--(40,0)--(0,30)--cycle,black+linewidth(1));
draw((20,0)--(20,15)--cycle,dashed);
draw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black + linewidth(1));
label("$A$",(0,0),SW);
label("$B$",(40,0),SE);
label("$C$",(0,30),NW);
label("$D$",(20,0),S);
[/asy]

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