
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: one white and one gray, each having integer side lengths. She noted down the areas of these two rectangles in her notebook.

She then overlaid the rectangles as shown in the picture. This created three new rectangles, and Dasha also noted the areas of these three rectangles in her notebook.

Calculate the length and width of the strip if the sum of all five numbers in Dasha's notebook is equal to 43. Answers can be entered in any order.

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