
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

On a circular road, there are four gas stations: $A, B, C,$ and $D$. The distance between $A$ and $B$ is $50$ km, between $A$ and $C$ is $40$ km, between $C$ and $D$ is $25$ km, and between $D$ and $A$ is $35$ km (all distances are measured along the shortest path on the circular road).

a) Provide an example of the arrangement of the gas stations (with the indicated distances between them) that satisfies the given conditions.

b) Find the distance between $B$ and $C$ (indicate all possibilities).

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