
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
Dasha cut a rectangular strip of paper into two rectangles: a white one and a gray one, each of which has integer side lengths. She recorded the areas of these two rectangles in her notebook.

Then, she placed the rectangles over each other as shown in the diagram. This resulted in three new rectangles, and Dasha also recorded their areas in her notebook.

Calculate the length and width of the strip, given that the sum of all five numbers in Dasha's notebook is 43. Answers can be provided in any order.

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