
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

A forgetful 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, tickets for an instant lottery are being sold for 10 rubles each. Each ticket has a 10% probability ($p=0.1$) of winning 30 rubles, and there are no other prizes. The scientist decides to take the risk since he has nothing to lose. Find the probability that the forgetful scientist will win enough money to buy a bus ticket.

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