
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
Three compressor stations are not located on the same line but are connected by straight roads. The distance from the first station to the third through the second is four times longer than the direct path between them; the distance from the first station to the second through the third is \(a\) km longer than the direct path; the distance from the second station to the third through the first is 85 km. Determine all values of \(a\) for which the specified arrangement of the compressor stations is possible. Calculate the distances between the compressor stations for \(a = 5\).

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