
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
There are $n$ ($n \geqslant 2$) cards, each with a different real number written on it. These $n$ numbers are all distinct. The cards are arbitrarily divided into two piles (each pile must have at least one card). It is always possible to take one card from the first pile and place it in the second pile, and then take one card from the second pile and place it in the first pile (it can be the same card), such that the sum of the numbers on the cards in each pile is equal to 0. Find the maximum possible value of $n$.

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