
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 positive integer \( n \geq 3 \) and a sequence of \( n \) different real numbers \(\left(a_{1}, a_{2}, \cdots, a_{n}\right)\) whose sum is positive. If a permutation \(\left(b_{1}, b_{2}, \cdots, b_{n}\right)\) satisfies \( b_{1}+b_{2}+\cdots+b_{k} > 0 \) for every \( k = 1, 2, \cdots, n \), then this permutation is called good. Determine the minimum number of such good permutations.

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