
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
Three concentric circles have radii $r_1$, $r_2$, and $r_3$ such that $r_1 < r_2 < r_3$. The area of the region between the first and second circles is twice the area of the region between the second and third circles. If the area of the largest circle is 3 times the area of the region between the first and the second circles, find the ratio $r_3:r_2:r_1$.

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