
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
The Pythagorean theorem first appeared in the book "Zhou Bi Suan Jing" by the mathematician Zhang Qiujian: "The width is 3, the height is 4, and the diagonal is 5." Observing the following Pythagorean numbers: 3, 4, 5, 5, 12, 13, 7, 24, 25, ..., the characteristics of these Pythagorean numbers are: the width is an odd number, and the difference between the diagonal and the height is 1. Plato studied a class of Pythagorean numbers where the width is an even number, and the difference between the diagonal and the height is 2, such as: 6, 8, 10, 8, 15, 17, ... If the width of this type of Pythagorean number is $2m$ ($m\geqslant 3$, $m$ is a positive integer), then its diagonal is ____ (express the result in terms of $m$).

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