
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
Gauss was a famous German mathematician, one of the founders of modern mathematics, and was known as the "Prince of Mathematics." In order to commemorate the mathematician Gauss, we define the floor function $y=\left[x\right]$, $x\in R$ as the Gauss function, where $\left[x\right]$ represents the largest integer not exceeding $x$, for example, $\left[1.9\right]=1$, $\left[-1.3\right]=-2$. Given an arithmetic sequence $\{{a}_{n}^{2}\}$ where $a_{n} \gt 0$, ${a}_{1}^{2}=3$, ${a}_{3}^{2}=5$, find $[\frac{1}{{a}_{1}+{a}_{2}}+\frac{1}{{a}_{2}+{a}_{3}}+\ldots +\frac{1}{{a}_{97}+{a}_{98}}]=\_\_\_\_\_\_$.

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