
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 that $a > 2$ and $b > 2$, and the equation $\frac{1}{2}\log_{2}(a+b)+\log_{2} \frac{ \sqrt {2}}{a}= \frac{1}{2}\log_{2} \frac {1}{a+b}+\log_{2} \frac {b}{ \sqrt {2}}$ holds, find the value of $\log_{2}(a-2)+\log_{2}(b-2)$.

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