
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
A passenger train travels from point $A$ to point $B$ at a speed of $30 \text{ km/h}$. A fast train departs from $A$ towards $B$ at a speed of $60 \text{ km/h}$ and usually overtakes the passenger train at point $B$. Due to a technical problem, after covering $\frac{2}{3}$ of the distance, the passenger train continues at half its original speed, leading the fast train to overtake it $271/9$ km before reaching $B$. What is the distance between $A$ and $B$?

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