
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
Anya and Borya are playing "Battleship" with the following rules: 29 distinct points on a circle are chosen and numbered clockwise with natural numbers from 1 to 29. Anya draws a ship - an arbitrary triangle with vertices at these points. Let's call a "shot" the choice of two distinct natural numbers \( k \) and \( m \) from 1 to 29. If the segment with endpoints at points numbered \( k \) and \( m \) has at least one common point with Anya's triangle, the ship is considered "hit." Borya makes a "volley" - several shots simultaneously. Anya has drawn a ship and shown it to Borya. They noticed that any "volley" of \( K \) different shots always hits Anya's ship. Indicate any configuration of Anya's ship where the value of \( K \) is minimal.

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