
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
Ten people are sitting around a rectangular table, each holding a fair coin. All ten people flip their coins and those who flip heads stand while those who flip tails remain seated. Additionally, if a person stands, the person immediately to their left must stand if they also flipped a head, essentially forming standing pairs. What is the probability that there are no standing pairs at the table?
**A)** $\frac{15}{128}$
**B)** $\frac{1}{16}$
**C)** $\frac{31}{128}$
**D)** $\frac{49}{250}$
**E)** $\frac{63}{256}$

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