
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
Cities \( A \), \( B \), and \( C \) along with the straight roads connecting them form a triangle. It is known that the direct path from \( A \) to \( B \) is 200 km shorter than the detour through \( C \), and the direct path from \( A \) to \( C \) is 300 km shorter than the detour through \( B \). Find the distance between cities \( B \) and \( C \).

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