
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
Four red beads, two white beads, and one green bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color?
A) $\frac{1}{15}$
B) $\frac{2}{15}$
C) $\frac{1}{7}$
D) $\frac{1}{30}$
E) $\frac{1}{21}$

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