
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
Express the sum

$$
1 \cdot 2^{2} \cdot 3 + 2 \cdot 3^{2} \cdot 4 + \ldots + (n-2)(n-1)^{2} n
$$

in closed form, where $n$ is a natural number greater than three.

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