
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  $n$  be a positive integer such that there exist positive integers  $x_1,x_2,\cdots ,x_n$  satisfying   $$ x_1x_2\cdots x_n(x_1 + x_2 + \cdots + x_n)=100n. $$   Find the greatest possible value of  $n$ .

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