
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 $ABC$, with $AB = AC$, a circle is inscribed touching $AB$ at point $D$, $AC$ at point $E$, and $BC$ at point $F$. If line $DF$ is extended to meet $AC$ at point $G$ and $\angle BAC = 90^\circ$, and the length of segment $DF$ equals $6$ cm, calculate the length of $AG$.
A) $3\sqrt{2}$ cm
B) $4\sqrt{2}$ cm
C) $6\sqrt{2}$ cm
D) $5\sqrt{2}$ cm

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