
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 $$f(x)=\log_{a}\left(1- \frac {2}{x+1}\right)$$ (where $a>0$, $a\neq1$)  
(1) Write down the value range and monotonic intervals of the function $f(x)$ (no proof required).  
(2) Does there exist a real number $a$ such that the domain of $f(x)$ is $[m, n]$, and the range is $[1+\log_{a}n, 1+\log_{a}m]$? If it exists, find the range of the real number $a$; if not, explain why.

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