
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
Petya's favorite TV game is called "Lottery on the Couch." During the game, viewers can send SMS messages with three-digit numbers containing only the digits 1, 2, 3, and 4. At the end of the game, the host announces a three-digit number, also consisting only of these digits. An SMS is considered a winning one if the number in it differs from the host's number by no more than one digit (for example, if the host announces the number 423, then messages 443 and 123 are winning, but 243 and 224 are not).

Petya wants to send as few messages as possible so that at least one is guaranteed to be winning. How many SMS messages does he need to send?

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