
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 $f(x)=ax^{2}+bx+c$ where $(a > 0)$ has two zeros $1$ and $2$, and the sequence $\{x_{n}\}$ satisfies $x_{n+1}=x_{n}- \frac {f(x_{n})}{f'(x_{n})}$. Let $a_{n}=\ln \frac {x_{n}-2}{x_{n}-1}$, if $a_{1}= \frac {1}{2}$ and $x_{n} > 2$, then the general formula for the sequence $\{a_{n}\}$ is $a_{n}=$ ______.

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