
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 such that each warehouse can be reached from any other, possibly by traveling through several roads. Each warehouse contains $x_{1}, \ldots, x_{2011}$ kg of cement, respectively. In one trip, any amount of cement can be transported from one warehouse to another along a connecting road. Ultimately, the plan is to have $y_{1}, \ldots, y_{2011}$ kg of cement at the warehouses, respectively, with the condition that $x_{1} + x_{2} + \ldots + x_{2011} = y_{1} + y_{2} + \ldots + y_{2011}$. What is the minimum number of trips required to execute this plan for any values of $x_{i}$ and $y_{i}$ and any road scheme?

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