
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 function $f_{k}(x)=a^{x}+ka^{-x}$, where $(k\in \mathbb{Z},a > 0$ and $a\neq 1)$.  
(I) If $f_{1}(1)=3$, find the value of $f_{1}\left( \frac {1}{2}\right)$;  
(II) If $f_{k}(x)$ is an odd function defined on $\mathbb{R}$, and $a > 1$, is there a real number $\lambda$ such that $f_{k}(\cos 2x)+f_{k}(2\lambda\sin x-5) < 0$ holds for any $x\in\left[0, \frac {2\pi}{3}\right]$? If it exists, find the range of values for the real number $k$; if not, explain why.

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