
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
The sequence $\{a\_n\}$ satisfies $a\_1=1$, $\sqrt{\frac{1}{a\_n^2}+1}=\frac{1}{a\_{n+1}}$, let $S\_n=a\_1^2+a\_2^2+...+a\_n^2$, if $S\_{2n+1}-S\_n \leqslant \frac{t}{30}$ holds for any $n \in \mathbb{N}^*$, then the minimum value of the positive integer $t$ is $\_\_\_\_\_\_\_\_$.

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