
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 $f(x)= \frac {1}{2}x^{2}-2ax-a\ln x$ for any $x_{1}$, $x_{2}$ ($x_{1}\neq x_{2}$) in the interval $(1,2)$, it holds that $\frac {f(x_{2})-f(x_{1})}{x_{2}-x_{1}} < 0$. Determine the range of $a$.

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