
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
Let the integer  $n \ge 2$  , and  $x_1,x_2,\cdots,x_n $  be real numbers such that  $\sum_{k=1}^nx_k$  be integer  .  $d_k=\underset{m\in {Z}}{\min}\left|x_k-m\right| $ ,  $1\leq k\leq n$  .Find the maximum  value of  $\sum_{k=1}^nd_k$ .

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