
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 equilateral triangle \(ABC\) with a side length of \(8 \, \text{cm}\), point \(D\) is the midpoint of side \(BC\), and point \(E\) is the midpoint of side \(AC\). Point \(F\) lies on the segment \(BC\) such that the area of triangle \(ABF\) is equal to the area of quadrilateral \(ABDE\).

Calculate the length of segment \(BF\).

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