
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
Given an integer  $n\geq 2$ , determine the maximum value the sum  $x_1+\cdots+x_n$  may achieve, as the  $x_i$  run through the positive integers, subject to  $x_1\leq x_2\leq \cdots \leq x_n$  and  $x_1+\cdots+x_n=x_1 x_2\cdots x_n$ .

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