
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
China Mathematical Olympiad 2018 Q6
Given the positive integer  $n ,k$   $(n>k)$  and  $ a_1,a_2,\cdots ,a_n\in (k-1,k)$  ,if positive number  $x_1,x_2,\cdots ,x_n$  satisfying:For any set  $\mathbb{I} \subseteq  \{1,2,\cdots,n\}$  , $|\mathbb{I} |=k$ ,have  $\sum_{i\in \mathbb{I}  }x_i\le \sum_{i\in \mathbb{I}  }a_i$  , find the maximum value of  $x_1x_2\cdots  x_n.$ 

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