
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
Triangle $ABC$ is a right triangle with $AC=3$, $AB=4$, and $BC=5$. A circle is inscribed within the triangle, tangential to all three sides at points $D$, $E$, and $F$, corresponding to sides $AC$, $AB$, and $BC$ respectively. If $DE$ is extended to meet $BC$ at $G$, find the length of $BG$.
A) $2$
B) $3$
C) $4$
D) $1$

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