
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 $f(n)=1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{n}$ ($n\in \mathbb{N}^{*}, n\geq 4$), after calculation, it is found that $f(4) > 2$, $f(8) > \frac{5}{2}$, $f(16) > 3$, $f(32) > \frac{7}{2}$, $\ldots$. Observing the above results, a general conclusion can be induced that $f(2^{n+1}) > \_\_\_\_\_\_$ ($n\in \mathbb{N}^{*}$).

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