
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 outside of circle $C$. A line segment is drawn from $Q$ such that it is tangent to circle $C$ at point $Z$. Meanwhile, a secant from $Q$ intersects $C$ at points $X$ and $Y$, such that $QX < QY$. If $QX = 5$ and $QZ = 2(QY - QX)$, find the length of $QY$.

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