
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 batch of goods is transported by 17 trains from city $A$ to city $B$ at a uniform speed of $v$ kilometers per hour. The distance between city $A$ and city $B$ along the railway is 400 kilometers. For safety reasons, the distance between any two trains must be no less than $\left(\frac{v}{20}\right)^2$ kilometers. Assuming the length of the trains is negligible, determine the minimum time required for all the goods to be transported from the first train's departure until they reach city $B$.

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