
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 birds land on a  $10$ -meter-long wire, each at a random point chosen uniformly along the wire. (That is, if we pick out any  $x$ -meter portion of the wire, there is an  $\tfrac{x}{10}$  probability that a given bird will land there.) What is the probability that every bird sits more than one meter away from its closest neighbor?

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