
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

On a coordinate plane, a square \( K \) is marked with vertices at points \((0,0)\) and \((10,10)\). Inside this square, depict the set \( M \) of points \((x, y)\) whose coordinates satisfy the equation

\[ [x] = [y], \]

where \([a]\) denotes the integer part of number \(a\) (that is, the largest integer not exceeding \(a\); for example, \([10]=10, [9.93]=9, [1 / 9]=0, [-1.7]=-2\)). What part of the area of square \( K \) does the area of set \( M \) constitute?

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