
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 certain country, there are 100 cities (consider the cities as points on a plane). In a directory, there is a record of the distance between every pair of cities (a total of 4950 records).

a) If one record is erased, can it always be uniquely restored using the remaining records?

b) Suppose \( k \) records are erased, and it is known that no three cities in this country lie on a single straight line. For what largest \( k \) can the erased records always be uniquely restored?

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