
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
The mathematicians of the Pythagorean school in ancient Greece studied various polygonal numbers, such as triangular numbers 1, 3, 6, 10..., where the nth triangular number is given by $\frac{n^2+n}{2}$. Denote the nth k-sided polygonal number as N(n, k) (k ≥ 3). Some expressions for the nth number in k-sided polygonal numbers are listed below:

Triangular numbers: N=(n,3)=$\frac{1}{2}$n^2$+\frac{1}{2}$n
Square numbers: N=(n,4)=$\frac{2}{2}$n^2$+0n
Pentagonal numbers: N=(n,5)=$\frac{3}{2}$n^2$-\frac{1}{2}$n
Hexagonal numbers: N(n,6)=$\frac{4}{2}$n^2$-\frac{2}{2}$n

Based on this, predict N(8, 8).

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