
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 parallelogram $ABCD$, extend side $AD$ and place a point $F$ on the extension. Line $BF$ intersects diagonal $AC$ at point $E$ and side $DC$ at point $G$. Given $EF = 45$ and $EG = 15$, find the length of segment $BG$.

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