
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 $[x]$ represents the largest integer not greater than $x$, and the function $f(x) = \left[\log_{2} \frac{2^{x} + 1}{9}\right]$, the following conclusions are obtained:

Conclusion 1: When $2 < x < 3$, $f(x)_{\max} = -1$.

Conclusion 2: When $4 < x < 5$, $f(x)_{\max} = 1$.

Conclusion 3: When $6 < x < 7$, $f(x)_{\max} = 3$.

...

Following this pattern, Conclusion 6 is ________.

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