
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 cities as points on a plane). For each pair of cities, there is a record in a directory that states the distance between them (a total of 4950 records).

a) One record has been erased. Is it always possible to uniquely restore it using the remaining records?

b) Suppose $k$ records have been erased, and it is known that in this country no three cities lie on the same line. What is the maximum value of $k$ such that it is always possible to uniquely restore the erased records?

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