
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
$X$ is a set of 9 positive integers. Let $E \subseteq X$, and $S(E)$ be the sum of the elements of set $E$. Let $n$ be the maximum value of an element in $X$. Find the value of $n$ such that there exist at least two subsets $A$ and $B$ of $X$ where $S(A) = S(B)$.

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