
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 children play a "tangling" game: they stand in a circle and move toward the center with eyes closed and arms outstretched. Each child grabs the hand of someone else with both hands. Then, they open their eyes and start "untangling" themselves by moving under each other's arms, stepping over each other's hands, etc. (everyone is sufficiently flexible) without letting go of each other's hands. In what percentage of all cases is it true that if at one point two neighboring children let go of each other's hands, the ten children still holding hands form a single connected chain?

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