
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 a set \(A\) of 10 distinct real numbers, a set \(A(5)\) can be constructed, consisting of all possible sums of five distinct numbers from the set \(A\). Do there exist two different sets \(A\) and \(B\) such that the sets \(A(5)\) and \(B(5)\) are identical?

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