
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
From point $P$, there are two ways to get to city $B$: either walk the $PB$ route, or walk to city $A$ and then take the train to $B$. Which points make it preferable to choose the first option, and which points make it preferable to choose the second option if you want to reach $B$ as quickly as possible? The walking speed is $5 \mathrm{~km/h}$, the train speed is $50 \mathrm{~km/h}$, and the distance between $A$ and $B$ is $20 \mathrm{~km}$.

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