
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 two sequences:

$$
\begin{array}{cccccc}
1, & 2, & 3, & \ldots, & \mathrm{n}-1, & \mathrm{n}, \\
2 \mathrm{n}-1, & 2 \mathrm{n}-3, & 2 \mathrm{n}-5, & \ldots, & 3, & 1
\end{array}
$$

calculate the sum of the products of the corresponding numbers in each sequence.

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