
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 located such that they are not on the same straight line but connected by straight roads. The distance from the first station to the third, passing through the second, is three times longer than the direct path between them. The distance from the first station to the second, passing through the third, is $a$ km longer than the direct path between them. The distance from the second station to the third, passing through the first, is 60 km. Determine all values of $a$ for which such an arrangement of compressor stations would be possible. Calculate the distances between the compressor stations for $a = 42$.

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