
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 people simultaneously step onto an escalator from opposite ends. The escalator is moving down at a speed of \( u = 1.5 \text{ m/s} \). The person moving down has a speed of \( v = 3 \text{ m/s} \) relative to the escalator, and the person moving up has a speed of \( \frac{2v}{3} \) relative to the escalator. At what distance from the lower end of the escalator will they meet? The length of the escalator is \( l = 100 \text{ m} \).

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