
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 room, two square carpets were brought in, with the side of one carpet being twice the side of the other. When they were placed in opposite corners of the room, they overlapped by $4 \ \mathrm{m}^{2}$. When they were placed in adjacent corners, they overlapped by $14 \ \mathrm{m}^{2}$. What are the dimensions of the room?

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