
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
Consider the Harmonic Table 
\[\begin{array}{c@{\hspace{15pt}}c@{\hspace{15pt}}c@{\hspace{15pt}}c@{\hspace{15pt}}c@{\hspace{15pt}}c@{\hspace{15pt}}c}&&&1&&&&&\tfrac12&&\tfrac12&&&\tfrac13&&\tfrac16&&\tfrac13&\tfrac14&&\tfrac1{12}&&\tfrac1{12}&&\tfrac14&&&\vdots&&&\end{array}\] where  $a_{n,1}=1/n$  and \[a_{n,k+1}=a_{n-1,k}-a_{n,k}.\] Find the remainder when the sum of the reciprocals of the  $2007$  terms on the  $2007^\text{th}$  row gets divided by  $2008$ .

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