
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
Given that the sum of the reciprocals of the roots of the equation $40x^{2}+39x-1=0$ forms the m-th term of the arithmetic sequence $1,3,5,\cdots$, and the product of the reciprocals of the roots forms the sum of the first n terms of the geometric sequence $2,-6,18,\cdots$, calculate the value of $m+n$.

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