
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  $k\ge2$  be an integer. Find the smallest integer  $n \ge k+1$  with the property that there exists a set of  $n$  distinct real numbers such that each of its elements can be written as a sum of  $k$  other distinct elements of the set.

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