
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
Suppose in a right triangle $DEF$ with the right angle at $E$ and $DF = \sqrt{85}$, $DE = 7$. A circle is drawn with its center on $DE$ such that the circle is tangent to $DF$ and $EF$. Let $Q$ be the point where the circle and side $DF$ meet. Determine the length of $FQ$.

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