
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

Scatterbrained Scientist has only 20 rubles left, but he needs to buy a bus ticket to get home, which costs 45 rubles. Near the bus stop, instant lottery tickets are being sold for exactly 10 rubles each. With a probability of $p = 0.1$, a ticket contains a prize of 30 rubles, and there are no other prizes. The Scientist decided to take a risk since he has nothing to lose. Find the probability that Scatterbrained Scientist will be able to win enough money to buy the bus ticket.

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