
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
A circle with area  $40$  is tangent to a circle with area  $10$ . Let R be the smallest rectangle containing both circles. The area of  $R$  is  $\frac{n}{\pi}$ . Find  $n$ .

[asy]
defaultpen(linewidth(0.7)); size(120);
real R = sqrt(40/pi), r = sqrt(10/pi);
draw(circle((0,0), R)); draw(circle((R+r,0), r));
draw((-R,-R)--(-R,R)--(R+2*r,R)--(R+2*r,-R)--cycle);[/asy]

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