
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
A \(41 \times 41\) battlefield is divided into 1681 unit squares. A tank is hidden in one of these unit squares. A bomber conducts airstrikes on the battlefield, bombing one unit square at a time. If a bomb falls on a unit square without a tank, the tank stays put. If the tank is hit, it moves to an adjacent unit square (two squares are "adjacent" if they share a common side). The tank needs to be hit twice to be destroyed. Throughout the process, the bomber pilot has no knowledge of the tank's position or whether it has been hit. Find the minimum number of bombings required to ensure the tank is destroyed.

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