
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
A rectangular piece of paper is folded in such a way that one of its vertices falls on the midpoint of one of its shorter edges. If the two shaded triangles are congruent (all three sides, angles, and areas are equal), and the length of the shorter edge of the rectangle before folding is 12 cm, what is the length of $\mathrm{BF}$ in centimeters?

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