
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
If $a^{2}+b^{2}=c^{2}$ $(a,b,c\in\mathbb{N}^{*})$, we call $a$, $b$, $c$ a Pythagorean triple. The following are several groups of Pythagorean triples: $3$, $4$, $5$; $5$, $12$, $13$; $7$, $24$, $25$; $9$, $40$, $41$. By analogy, the three numbers of the fifth group of Pythagorean triples are \_\_\_\_\_\_\_.

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