
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 \\(F(x,y)=y^{x}(x>0,y>0)\\) and the sequence \\(\{a_{n}\}\\) defined by \\(a_{n}= \dfrac {F(n,2)}{F(2,n)}(n\in\mathbb{N}^{*})\\), determine the value of \\(a_{k}\\) such that for any positive integer \\(n\\), \\(a_{n}\geqslant a_{k}(k\in\mathbb{N}^{*})\\).

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