
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 $f(x)=x^{2}-ax+a (x\in R)$, it has exactly one zero point in its domain. There exist $0 < x_{1} < x_{2}$ such that the inequality $f(x_{1}) > f(x_{2})$ holds. For $n\in N^{*}$, $f(n)$ is the sum of the first $n$ terms of the sequence $\{a_{n}\}$. All positive integers $k$ for which $c_{k}⋅c_{k+1} < 0$ in the sequence $\{c_{n}\}$ (where all terms are non-zero) are called the variation count of the sequence $\{c_{n}\}$. If $c_{n}=1- \frac {4}{a_{n}}$, find the variation count of the sequence $\{c_{n}\}$.

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