
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
 $n$  is a fixed natural number. Find the least  $k$  such that for every set  $A$  of  $k$  natural numbers, there exists a subset of  $A$  with an even number of elements which the sum of it's members is divisible by  $n$ .

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