
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 \( Q(x) = x^2 - 5x - 7 \). A real number \( x \) is chosen at random from the interval \( 4 \le x \le 18 \). The probability that \( \lfloor\sqrt{Q(x)}\rfloor = \sqrt{Q(\lfloor x \rfloor)} \) is given by \( \frac{\sqrt{p} + \sqrt{q} - r}{s} \) where \( p \), \( q \), \( r \), and \( s \) are integers. Find \( p + q + r + s \).

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