
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 the sequence $a_i = \frac{1}{i}$ for $i=1,2,...,n$, and the sequence $a_i^{(n)} = n\cdot a_i$ for $i=1,2,...,n$, determine the value of the expression $a_1^{(n)}a_2^{(n)} + a_2^{(n)}a_3^{(n)} + ... + a_{n-1}^{(n)}a_n^{(n)}$.

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