
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

2011 warehouses are connected by roads in such a way that from any warehouse you can reach any other, possibly passing through several roads. There are $x_{1}, \ldots, x_{2011}$ kg of cement in the warehouses, respectively. In one trip, an arbitrary amount of cement can be transported from one warehouse to another along the connecting road. As a result, the plan is to have $y_{1}, \ldots, y_{2011}$ kg of cement in the warehouses, respectively, where:

$$
x_{1} + x_{2} + \cdots + x_{2011} = y_{1} + y_{2} + \cdots + y_{2011}
$$

What is the minimum number of trips required to implement the plan for any values of $x_{i}$ and $y_{i}$ and any road scheme?

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