
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
Let's call a "boat" a trapezoid $\square$ with bases 1 and 3, created by attaching two small triangles (half-squares) to the opposite sides of a unit square. A boat is positioned invisibly within a $100 \times 100$ square (it can be rotated, doesn't go beyond the square's boundaries, and its central cell entirely lies within one of the square's cells). A single shot can cover any triangular half of a cell. If a shot intersects the interior of the boat (meaning the intersection between the shot's triangle and the boat has a non-zero area), the boat is considered sunk. What is the minimum number of shots needed to guarantee that the boat will be sunk?

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