
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 \( f(n) = \sum_{k=1}^{n} \frac{1}{k} \). Then there exist constants \(\gamma\), \(c\), and \(d\) such that
\[ f(n) = \ln (n) + \gamma + \frac{c}{n} + \frac{d}{n^{2}} + O\left(\frac{1}{n^{3}}\right), \]
where the \( O\left(\frac{1}{n^{3}}\right) \) indicates terms of order \( \frac{1}{n^{3}} \) or lower. Compute the ordered pair \((c, d)\).

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