
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
Two cars travel along a circular track  $n$  miles long, starting at the same point. One car travels  $25$  miles along the track in some direction. The other car travels  $3$  miles along the track in some direction. Then the two cars are once again at the same point along the track. If  $n$  is a positive integer, find the sum of all possible values of  $n.$ 

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