
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  $M$  be the set of the integer numbers from the range  $[-n, n]$ . The subset  $P$  of  $M$  is called a *base subset* if every number from  $M$  can be expressed as a sum of some different numbers from  $P$ . Find the smallest natural number  $k$  such that every  $k$  numbers that belongs to  $M$  form a base subset.

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