
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(x)=x-\frac{2}{x},x\in \[ 1,2 \]$, and $g(x)=a\cos \frac{\pi x}{2}+11-2a,(a\ne 0)$. For any ${{x}\_{1}}\in \[ 1,2 \]$, there always exists ${{x}\_{2}}\in \[ 0,1 \]$, such that $g({{x}\_{2}})=f({{x}\_{1}})$ holds true. Determine the range of values for $a$.

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