
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
Let $P$ be a point chosen uniformly at random inside a unit square with vertices at $(0,0)$, $(1,0)$, $(1,1)$, and $(0,1)$. Define a new fixed point $Q=(\frac{1}{2}, \frac{1}{2})$. Determine the probability that the slope of the line passing through points $P$ and $Q$ is greater than or equal to $1$. Express your answer as a fraction in the form $\frac{m}{n}$, where $m$ and $n$ are coprime positive integers. Find $m+n$.

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