
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
An oil tanker truck needs to transport gasoline from point $A$, an oil production site, to point $B$. The truck's maximum fuel capacity is exactly equal to the amount of fuel needed for a round trip between $A$ and $B$ (the truck must return to $A$). Therefore, gas cannot be transported directly to $B$. If an intermediate station $C$ is set up between $A$ and $B$, then:

(1) When $C$ is located $\frac{1}{3}$ of the way from $A$ to $B$, what is the most economical method to transport gasoline from $A$ to $B$ so that the maximum amount of gasoline is received at $B$? What is the transport efficiency rate $\left(\frac{\text{amount of gasoline received at } B}{\text{amount of gasoline shipped from } A}\right)$ in this case?

(2) Where should the intermediate station be located to maximize the transport efficiency rate? What is the efficiency rate in this case?

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