
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 Spring Festival of 2023, to promote consumption and drive economic growth, Shapingba District opened a special product promotion on the pedestrian street. Xiaoqiang from Class 1 of Grade 7 at our school plans to divide a shop into three areas, A, B, and C, to operate three kinds of goods. After Dad planned the area of the three regions, Xiaoqiang actively helped Dad divide the area of the three regions. After the division was completed, Dad found that Xiaoqiang carelessly misallocated $10\%$ of the original area of region A to region B, and $50\%$ of the original area of region B to region A, resulting in the current area of region B accounting for $40\%$ of the sum of the areas of regions A and B, while the area of region C was not misallocated. In order to coordinate the area ratios of the three regions, Dad had to divide $50\%$ of the area of region C into two parts and allocate them to the current regions A and B. If after Dad's division, the area ratios of regions A, B, and C are $2:1:1$, then the ratio of the area allocated from region C to region B to the total area of the shop is ______.

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