
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
Three circles with centers $P$, $Q$, and $R$ each have radii $s$, where $2 < s < 3$. The distance between each pair of centers is $3$. If $Q'$ is the intersection of circle $P$ with circle $R$ that lies outside circle $Q$, and $R'$ is the intersection of circle $P$ with circle $Q$ that lies outside circle $R$, what is the length of segment $Q'R'$?
A) $1.5s - 2.25$
B) $s + \sqrt{6(s - 1)}$
C) $1.5 + \sqrt{6(s^2 - 2.25)}$
D) $2s - 3$
E) $s^2 - 1.5$

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