
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 the same straight line but are connected by straight 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 possible values of $a$ for which the given arrangement of compressor stations is feasible. Calculate the distances between the compressor stations when $a = 42$.



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