
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
Construct the sequence $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots, \frac{1}{n}$, and let $a_1, a_2, a_3, \ldots, a_n$ be the new sequence obtained by multiplying each term of the original sequence by $\frac{n}{2}$. Evaluate the sum $a_1a_2+a_2a_3+a_3a_4+\ldots+a_{n-1}a_n$.

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