
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 point $P(x, y)$ is randomly selected from the set $M={(x,y)∣(|x|−1)^2+(|y|−1)^2 < 4$, $x$, $y∈Z}$. If the probability that $xy≥k (k > 0)$ is $\frac{6}{25}$, what is the maximum value of $k$?

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