
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
Six ants initially stand on six vertices of a modified octahedral structure, where vertex $A$ connects to five other vertices ($B, C, D, E, F$) and vertex $F$ connects to three vertices ($A, B, C$), with $B, C, D, E$ forming a quadrilateral base. Each ant independently moves to one of its adjacent vertices with equal probability. What is the probability that no two ants land on the same vertex?
A) $\frac{160}{15625}$
B) $\frac{200}{15625}$
C) $\frac{220}{15625}$
D) $\frac{240}{15625}$
E) $\frac{250}{15625}$

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