
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 functions $$f(x)=(\log_{2}x)^{2}-2\log_{\frac{1}{2}}x+1$$ and $$g(x)=x^{2}-ax+1$$  
(1) Find the domain of the function $$y=f(\cos(x- \frac{\pi}{3}))$$;  
(2) If there exists $a \in \mathbb{R}$, such that for any $$x_{1} \in [\frac{1}{8}, 2]$$, there always exists a unique $x_{0} \in [-1, 2]$, making $f(x_{1})=g(x_{0})$ hold. Find the range of the real number $a$.

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