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

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