
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
In a game show, there are three doors, one of which has a prize behind it. The contestant can ask the host whether the prize is behind the left (or right) door. The contestant can ask multiple questions in any order about the chosen door, and each time the host will answer "yes" or "no". It is known that before the official competition, the contestant must inform the host of the number of times they will choose a door. The host can lie at most 10 times. How many questions does the contestant need to ask to be certain about the door hiding the prize?

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