
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 \(A\) to other locations, you can travel in two ways:

1. Start walking immediately.
2. Call a car, wait for a certain period, and then drive.

In each case, the method that requires less time is used. It turns out that:

\[
\begin{tabular}{|c|c|}
\hline Final point is & Total travel time required \\
\hline \(1 \text{ km}\) & 10 minutes \\
\(2 \text{ km}\) & 15 minutes \\
\(3 \text{ km}\) & \(17 \frac{1}{2}\) minutes \\
\hline
\end{tabular}
\]

The speeds of the pedestrian and the car, as well as the waiting time for the car, remain constant. How much time is needed to travel to a point 6 km away from \(A\)?

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