
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
Calculate $f(n) = 1 + \frac{1}{2} + \frac{1}{3} +…+ \frac{1}{n}$ (where $n \in \mathbb{N^*}$). Given that $f(2) = \frac{3}{2}, f(4) > 2, f(8) > \frac{5}{2}, f(16) > 3, f(32) > \frac{7}{2}$, conjecture an inequality for $f(2^n)$ when $n \geq 2$.

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