
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
A rectangular board of 8 columns has squares numbered beginning in the upper left corner and moving left to right. A student shades square 1, then skips one square and shades square 3, skips two squares and shades square 6, skips 3 squares and shades square 10, and continues in this way, skipping $n-1$ squares and shading the $\left\lfloor\frac{n(n+1)}{2}\right\rfloor$th square for $n=1,2,3,\ldots$. What is the number of the square that is first shaded in the 8th column?

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