
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
Two classes of elementary school students are going to the Children's Palace for an activity, but there is only one car for transportation. When the first class of students departs from the school by car, the second class starts walking. The car drops the first class off at some point along the way to continue walking and returns immediately to pick up the second class of students, then drives directly to the Children's Palace. The students walk at a speed of 4 kilometers per hour. The car drives at 40 kilometers per hour when carrying students and 50 kilometers per hour when empty. To ensure that both classes of students arrive at the Children's Palace at the same time, what fraction of the total distance does the first class walk? (Ignore the time taken for students to board and disembark the car.)

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