
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 segment is drawn from $Q$, tangent to circle $C$ at point $R$, and a different secant from $Q$ intersects $C$ at points $D$ and $E$ such that $QD < QE$. If $QD = 5$ and the length of the tangent from $Q$ to $R$ ($QR$) is equal to $DE - QD$, calculate $QE$.

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