
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
Absent-minded Scientist has 20 rubles left and needs to buy a bus ticket to go home, which costs 45 rubles. Near the bus stop, instant lottery tickets are being sold for 10 rubles each. With a probability of $p=0.1$, a lottery ticket wins 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 the Absent-minded Scientist will be able to win enough money to buy the bus ticket.

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