
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
Through vertex $A$ of parallelogram $ABCD$, a line is drawn that intersects the diagonal $BD$, side $CD$, and line $BC$ at points $E$, $F$, and $G$, respectively. Find the length $ED$ if $FG : FE = 7$ and $BE = 8$. Round the answer to two decimal places if necessary.

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