
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
The towns \( A \), \( B \), and \( C \) are connected by straight roads. The distance from town \( A \) to the road connecting towns \( B \) and \( C \) is 100 km, and the sum of the distances from town \( B \) to the road connecting \( A \) and \( C \), and from town \( C \) to the road connecting \( A \) and \( B \), is 300 km. It is known that point \( D \) is equidistant from the roads connecting towns \( A \), \( B \), and \( C \) and lies within the area bounded by these roads. Any resident of all the towns uses no more than 1 liter of fuel for every 10 km of road. What is the maximum volume of fuel a motorist would need to reach any of the roads connecting the other towns from point \( D \)?

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