
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
There are coins of denominations 50 kopecks, 1 ruble, 2 rubles, 5 rubles, and 10 rubles. In a wallet, there are several coins. It is known that no matter which 20 coins are taken out of the wallet, among them there will be at least one 1-ruble coin, at least one 2-ruble coin, and at least one 5-ruble coin. What is the maximum number of coins possible in the wallet such that this condition holds?

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