
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 ancient Chinese mathematical masterpiece "Zhou Bi Suan Jing" records the phrase "multiply the legs and the base of a right triangle by themselves, add them together, and then take the square root of the sum," which is symbolically represented as $a^{2}+b^{2}=c^{2} (a,b,c \in \mathbb{N}^{*})$. We call $a$, $b$, and $c$ Pythagorean triples. Given several sets of Pythagorean triples: $3, 4, 5$; $5, 12, 13$; $7, 24, 25$; $9, 40, 41$, and so on, we can guess that the three numbers of the fifth set of Pythagorean triples are ______.

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