
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
Triangle $XYZ$ with a right angle at $Z$, $\angle YXZ < 45^\circ$ and $XY = 5$. Point $Q$ on $\overline{XY}$ is chosen such that $\angle YQZ = 2\angle YZQ$ and $ZQ = 2$. Find the ratio $\frac{YQ}{XQ}$ in the form of $a + b\sqrt{c}$, where $a$, $b$, $c$ are positive integers and $c$ is not divisible by the square of any prime. Determine $a+b+c$.

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