
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 having integer side lengths. She recorded the areas of these two rectangles in her notebook.

Then she overlaid the rectangles, as shown in the picture, resulting in three new rectangles. Dasha also recorded the areas of these three rectangles 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 entered in any order.

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