
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 $f(x)=\log_{a}x$ ($a > 0$ and $a \neq 1$) has its maximum value on the interval $[1,2]$ equal to the opposite number of the maximum value of the function $g(x)=- \frac {4}{x}$ on the interval $[1,2]$.  
$(1)$ Find the value of $a$;  
$(2)$ If the function $F(x)=f(x^{2}-mx-m)$ is decreasing on the interval $(-\infty,1- \sqrt {3})$, find the range of the real number $m$.

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