
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 trapezoid $ABCD$ with bases $AD$ and $BC$, a point $F$ lies outside the trapezoid along the extension of $AD$. $BF$ intersects diagonal $AC$ at $E$, and side $DC$ extends to $G$ such that $FG$ is parallel to $BC$. If $EF = 40$ and $GF = 30$, find $BE$.

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