
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 10 rows is numbered in a snaking pattern, starting in the upper left corner. In the first row, the squares are numbered from 1 to 10, in the second row from 20 to 11 (backwards), and so on alternating directions each row. A student shades square 1, then skips one square and shades square 3, skips two squares and shades square 6, skips three squares and shades square 10, continuing in this manner. Determine the number of the shaded square that is the first to ensure at least one shaded square in each row.

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