
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
The rectangle \(ABCD\) has side \(AB\) of length \(12 \, \text{cm}\) and side \(BC\) of length \(6 \, \text{cm}\). Point \(S\) is the center of the rectangle, and point \(F\) lies on side \(CD\). The quadrilateral \(BCFS\) has an area that is one third of the area of rectangle \(ABCD\).

Determine the length of segment \(CF\).

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