
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

There are 5 units of gasoline at location $A$, and location $B$ needs gasoline. A car transports gasoline from $A$ to $B$. The round trip oil consumption is exactly equal to the car's full load of gasoline, making it impossible to transport gasoline directly from $A$ to $B$. A storage station is set up at location $C$ as an intermediate point. First, cars ferry gasoline back and forth between $A$ and $C$, and then cars transport gasoline between $C$ and $B$.

(1) Suppose $AC = \frac{1}{3} AB$. How should transportation be organized to economically transport gasoline from $A$ to $B$ (to maximize the gasoline received at $B$)? What is the transportation efficiency at this time $\left(\frac{\text{Gasoline received at B}}{\text{Gasoline sent from A}}\right)$?

(2) Suppose $AC = d$. What value of $d$ maximizes the transportation efficiency? How should transportation be organized under these conditions?

(3) If two intermediate stations $C$ and $D$ are set up along the way with $AC = d_1$ and $CD = d_2$, what values of $d_1$ and $d_2$ maximize the transportation efficiency? How should transportation be organized in this case?

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