
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 ladder is formed by removing some consecutive unit squares of a $10\times 10$ chessboard such that for each $k-$th row ($k\in \{1,2,\dots, 10\}$), the leftmost $k-1$ unit squares are removed. How many rectangles formed by composition of unit squares does the ladder have?

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