
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 $a\in\mathbb{R}$, the function $f(x)=\log_{2}\left(\frac{1}{2^{x}}+a\right)$.  
(I) When $a=1$, solve the inequality $f(x) > 1$;  
(II) If the solution set of the equation $f(x)+2x=0$ with respect to $x$ contains exactly one element, find the range of values for $a$;  
(III) Let $a > 0$, if for any $t\in[-1,0]$, the sum of the maximum and minimum values of the function $f(x)$ in the interval $[t,t+1]$ is not greater than $\log_{2}6$, find the range of values for $a$.

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