
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
The diagram shows two concentric circles. The length of chord AB is 100 units, and chord AB is tangent to the smaller circle. Calculate the area of the shaded region between the two circles, expressing your answer in terms of $\pi$.

[asy]
defaultpen(linewidth(.8pt));
dotfactor=4;
filldraw(circle((0,0),60),gray);
filldraw(circle((0,0),40),white);
dot((0,0));

draw((-50,40)--(50,40));

label("$A$",(-50,40),W);
label("$B$",(50,40),E);
[/asy]

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