
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 situated on a straight line but are connected by direct roads. The distance from the first station to the third station via the second station is three times the direct path between them; the distance from the first station to the second station via the third station is $a$ km longer than the direct path; the distance from the second station to the third station via the first station is 60 km. Determine all values of $a$ for which the specified arrangement of the compressor stations would be possible. Calculate the distances between the compressor stations when $a=42$.

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