
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
In the sequence $\{a\_n\}$, $a\_1= \frac {1}{2},a\_{n+1}= \frac {na\_n}{(n+1)(na\_n+1)}(n\in\mathbb{N}^*)$, if the inequality $\frac {3}{n^{2}}+ \frac {1}{n}+ta\_n\geqslant 0$ always holds true, then the range of the value of the real number $t$ is \_\_\_\_\_\_.

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