
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 7 horizontal and 13 vertical streets. A pair of horizontal streets and a pair of vertical streets form the rectangular border of the city, while the rest divide it into blocks that are in the shape of squares with a side length of 100 meters. Each block has an address consisting of two integers $(i ; j), i=1,2, \ldots, 6, j=1,2, \ldots, 12,$ representing the numbers of the streets that bound it on the bottom and on the left.

A taxi transports passengers from one block to another, adhering to the following rules:
1. Pickup and drop-off can happen at any point on the boundary of a block as per the passenger's choice.
2. Entering the interior of a block is prohibited.
3. The taxi takes the shortest path.
4. For every 100 meters of distance traveled, the fare is 1 coin (the distance is 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 for a ride from block $(4,2)$ to block $(1,9)$ that the driver can charge the passenger, adhering to the rules?

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