
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 the first five terms of a sequence $\{a\_n\}$ are $0, \frac{\sqrt{3}}{3}, \frac{\sqrt{2}}{2}, \frac{\sqrt{15}}{5}, \frac{\sqrt{6}}{3}$, infer a general formula for the nth term based on the first four terms, and the fifth term should also satisfy the inference. Your inferred result for $a\_n=$ \_\_\_\_\_\_.

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