
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
In a right-angled triangle $DEF$ with $\angle DEF = 90^\circ$, side $DE = 6$ units, and side $EF = 8$ units. A circle is inscribed in the triangle, tangent to all three sides at points $A$, $B$, and $C$ respectively. Another smaller circle is externally tangent to side $EF$ at point $G$ and also tangent to the extension of side $DE$. Calculate the radius $r$ of the inscribed circle.
A) 1 unit
B) 2 units
C) 3 units
D) 4 units

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