
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 the integer part of the real number \(\frac{2+\sqrt{2}}{2-\sqrt{2}}\) is \(a\), and the decimal part is \(1 - b\), find the value of \(\frac{(b-1) \cdot (5-b)}{\sqrt{a^{2}-3^{2}}}\).

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