
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 a large square hall, two square rugs were brought in, with the side of one rug being twice the length of the side of the other. When they were placed in opposite corners of the hall, they overlapped an area of 4 m²; when they were placed in adjacent corners, they overlapped an area of 14 m². What are the dimensions of the hall?

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