
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
For a positive sequence $\{a_n\}$, the sum of the first $n$ terms is $S_n$, and there exists a positive number $t$, such that for any positive integer $n$, $$\sqrt {tS_{n}}= \frac {t+a_{n}}{2}$$ holds. If $$\lim_{n\rightarrow +\infty } \frac { \sqrt {S_{n}}}{a_{n}}<t$$, then the range of $t$ is \_\_\_\_\_\_\_\_\_\_\_\_.

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