
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 traveling from point $A$ to point $B$ at a speed of $30 \ \text{km/h}$ is overtaken by an express train, which also starts from point $A$ but departs later and travels at a speed of $60 \ \text{km/h}$. Under normal conditions, the express train catches up with the passenger train at point $B$. However, after traveling ${2}/{3}$ of the distance, the passenger train encounters a mechanical failure, reducing its speed to half of its original speed. As a result, the express train catches up to the passenger train $27 \  \text{km}$ before point $B$. What is the distance between points $A$ and $B$?

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