
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 an isosceles right triangle with each leg measuring $8$ units, a circle is inscribed. Calculate the radius, $r$, of the circle.
A) $6 - 4\sqrt{2}$
B) $8 + 4\sqrt{2}$
C) $8 - 4\sqrt{2}$
D) $10 - 6\sqrt{2}$

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