
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= \dfrac {1}{3}\\), and \\( \dfrac {n}{a_n}= \dfrac {2a_{n-1}+n-1}{a_{n-1}}(n\in\mathbb{N}^*,n\geqslant 2)\\), then the general formula for the sequence \\(\{a_n\}\) is \\(a_n=\) ______.

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