
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
  $$ Problem 4: $$  The sum of  $5$  positive numbers equals  $2$ . Let  $S_k$  be the sum of the  $k-th$  powers of
these numbers. Determine which of the numbers  $2,S_2,S_3,S_4$  can be the greatest among them.

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