
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
An entry in a grid is called a saddle point if it is the largest number in its row and the smallest number in its column. Suppose that each cell in a \(3 \times 3\) grid is filled with a real number, each chosen independently and uniformly at random from the interval \([0,1]\). Compute the probability that this grid has at least one saddle point.

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