
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

In the coordinate plane, a square $K$ with vertices at points $(0,0)$ and $(10,10)$ is given. Inside this square, illustrate the set $M$ of points $(x, y)$ whose coordinates satisfy the equation

$$
[x] < [y]
$$

where $[a]$ denotes the integer part of the number $a$ (i.e., the largest integer not exceeding $a$; for example, $[10]=10,[9.93]=9,[1 / 9]=0,[-1.7]=-2$). What portion 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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