
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

In a city, there are 10 parallel streets running from north to south, and 10 streets running from west to east, forming a $9 \times 9$ grid. There is a square at each intersection, totaling 100 squares. The distance between any two adjacent squares along a street is 1 km. A walking distance pharmacy is defined as a pharmacy that can be reached by walking no more than 3 km along the streets. The Ministry of Health wants to install pharmacies on some squares so that any person walking along any street, regardless of the direction of travel, will get closer to a walking distance pharmacy. Is it enough to have 12 pharmacies for this purpose?

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