
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 via the second is three times longer than the direct path between them; the distance from the first station to the second via the third is $a$ km longer than the direct path; the distance from the second station to the third via the first is 60 km. Determine all values of $a$ for which the described arrangement of compressor stations is possible. Calculate the distances between the compressor stations when $a=30$.

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