
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 \\(n\\) be a positive integer, and \\(f(n) = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n}\\). It is calculated that \\(f(2) = \frac{3}{2}\\), \\(f(4) > 2\\), \\(f(8) > \frac{5}{2}\\), and \\(f(16) > 3\\). Observing the results above, according to the pattern, it can be inferred that \\(f(128) > \_\_\_\_\_\_\_\_．

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