
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
Let $f(n) = 1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n} \ (n \in \mathbb{N}^*)$, compute $f(2) = \frac{3}{2}$, $f(4) > 2$, $f(8) > \frac{5}{2}$, $f(16) > 3$, ..., observe that according to the above rules, it can be inferred that $f(2048) >$           .

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