
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
Given a sequence ${\{(a_{n})\}}$ where each term is greater than zero, the first term $a_{1}$ equals 1, and the sum of the first $n$ terms $S_{n}$ satisfies $S_{n} \sqrt{{S}_{n-1}} -S_{n-1} \sqrt{{S}_{n}}=2 \sqrt{{S}_{n}{S}_{n-1}} (n \in N^{*}, n \geqslant 2)$, calculate the value of $a_{81}$.

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