
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 a single straight line, but they are connected by straight roads. The distance from the first station to the third station via the second station is four times the straight-line distance between the first and third stations; the distance from the first station to the second station via the third station is \(a\) kilometers longer than the straight-line distance between them; the distance from the second station to the third station via the first station is 85 km. Determine all possible values of \(a\) for which the described arrangement of compressor stations is possible. Calculate the distances between the compressor stations when \(a = 5\).

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