
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
Pinocchio must successfully overcome 9 different obstacles to become a real boy. It's a challenging task; if he fails at any obstacle, he must return to the previous one and try again. If he fails at the very first obstacle, he remains a wooden puppet forever. Pinocchio does not learn from his failures, so the probability of success at each obstacle remains constant at $\frac{1}{10}, \frac{2}{10}, \ldots, \frac{9}{10}$, regardless of the number of attempts. In what order should the Blue Fairy arrange the obstacles so that Pinocchio has the greatest chance of turning into a real boy, and what is the success probability in that case?

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