
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
Let $a\in R$, the function $f\left(x\right)=\left\{\begin{array}xcos(2πx-2πa)&x＜a\\{x}^{2}-2(a+1)x+{a}^{2}+5&x≥a\end{array}\right.$ has exactly $6$ zeros in the interval $\left(0,+\infty \right)$. Find the range of values of $a$.

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