
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 the city "N," there are 12 horizontal and 16 vertical streets, forming a rectangular border for the city, while the remaining streets divide the city into blocks shaped as squares with a side length of 100 meters. Each block has an address consisting of two integers \((i; j)\), where \(i=1,2, \ldots, 11\) and \(j=1,2, \ldots, 15\), representing the numbers of the streets that border it from below and from the left. A taxi transports passengers from one block to another, adhering to the following rules: 

1. Passengers can board and alight at any point on the boundary of the block at their discretion.
2. It is forbidden to drive inside the block.
3. Transport occurs via the shortest route.
4. A fare of 1 coin is charged for every 100 meters traveled (with the distance rounded up to the nearest multiple of 100 meters in favor of the driver).

How many blocks are in the city? What is the maximum and minimum fare that the driver can charge for a ride from block \((7, 2)\) to block \((2, 1)\) without breaking the rules?

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