
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 \\(a_{i} > 0(i=1,2,3,…,n)\\), observe the following inequalities: \\( \dfrac {a_{1}+a_{2}}{2}\geqslant \sqrt {a_{1}a_{2}}\\); \\( \dfrac {a_{1}+a_{2}+a_{3}}{3}\geqslant \sqrt[3]{a_{1}a_{2}a_{3}}\\); \\( \dfrac {a_{1}+a_{2}+a_{3}+a_{4}}{4}\geqslant \sqrt[4]{a_{1}a_{2}a_{3}a_{4}}\\);  
\\(…\\)  
Following this pattern, when \\(n\in\mathbb{N}^*(n\geqslant 2)\\), \\( \dfrac {a_{1}+a_{2}+…+a_{n}}{n}\geqslant \\) ______.

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