
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 $a_1=1$, and the sum of the first $n$ terms $S_n$ satisfies $$S_{n} \sqrt {S_{n-1}}-S_{n-1} \sqrt {S_{n}}=2 \sqrt {S_{n}S_{n-1}}$$ ($n\in\mathbb{N}^*$, and $n\geq2$), calculate $a_{81}$.

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