
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
Vovochka approached a game machine, on the screen of which the number 0 was displayed. The rules of the game stated: "The screen shows the number of points. If you insert a 1-ruble coin, the number of points increases by 1. If you insert a 2-ruble coin, the number of points doubles. If you score 50 points, the machine gives a prize. If the resulting number is greater than 50, then all the points scored are lost." What is the minimum amount of rubles Vovochka needs to get the prize? Answer: 11 rubles.

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