
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
Nine horizontal and fifteen vertical streets form a total of $(9-1)(15-1)=112$ square blocks in city "N". Let points $A$ and $C$ on the map be the closest points of blocks $(2, 3)$ and $(5, 12)$ respectively. Then the path between them (according to the rules) has a length of $100(|5-2|+|12-3|-2)=1000$. One possible route is the path $A E C$. Now let $B$ and $D$ be the most distant points of the blocks. Then the path between them (according to the rules) has a length of $100(|5-2|+|12-3|+2)=1400$. One possible route is the path $B F D$. Therefore, the minimum number of coins is $c_{\text{min}}=1000/100=10$, and the maximum is $-c_{\max}=1400/100=14$.

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