
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
Consider a right triangle $XYZ$ where the right angle is at $Y.$ Let $XZ = \sqrt{85}$ and $XY = 7.$ A circle is drawn with its center on $XY$ such that the circle is tangent to $XZ$ and $YZ.$ If $Q$ is the point where the circle and side $XZ$ meet, determine the length of $ZQ.$

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