
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 \( Q \) be a point chosen uniformly at random within the unit square with vertices at \( (0,0), (1,0), (1,1) \), and \( (0,1) \). Determine the probability that the slope of the line connecting \( Q \) and the point \( \left(\frac{3}{4}, \frac{1}{4} \right) \) is less than or equal to \( 1 \). Express this probability as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are coprime integers, and find \( p+q \).

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