
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, where all the digits are distinct. Igor is trying to guess this number. In one turn, Igor can select several positions (digits) of the number, and Misha will tell him the digits in these positions in random order. The order in which Misha reports the digits is chosen by Misha. For example, if the number is 67890 and Igor asks for the digits in positions 1 and 5, Misha may reply with "6 and 0" or "0 and 6." What is the minimum number of turns Igor needs to guarantee that he can determine the entire number? Points for the problem: 13.

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