
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
Misha has thought of a five-digit number, all of whose digits are distinct, and Igor is trying to guess it. In one turn, Igor can choose several digits of the number, and Misha will inform him of the digits at those places in random order. The order in which the digits are revealed is chosen by Misha. For example, if the number thought of is 67890, and Igor asks about the digits in positions 1 and 5, then Misha could answer "6 and 0" or "0 and 6". What is the minimum number of turns Igor will need to guarantee to find out the number?

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