
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 city "N", there are 10 horizontal and 12 vertical streets. A pair of horizontal and a pair of vertical streets form the rectangular boundary of the city, while the rest divide it into blocks shaped like squares with a side length of 100 meters. Each block has an address consisting of two integers \((i, j)\), \(i = 1, 2, \ldots, 9\), \(j = 1, 2, \ldots, 11\), representing the numbers of the streets that bound it from below and the left. A taxi transports passengers from one block to another, observing the following rules:

1. Pickup and drop-off are carried out at any point on the block's boundary at the passenger's request.
2. It is prohibited to enter inside the block.
3. Transportation is carried out by the shortest path.
4. For every 100 meters of travel, a fare of 1 coin is charged (with distance rounded up to the nearest multiple of 100 meters in favor of the driver).

How many blocks are there in the city? What is the maximum and minimum fare the driver can request for a ride from block \((7,1)\) to block \((2,10)\) without violating the rules?

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