
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
One of the numbers \(a, b, c\) is positive, one is negative, and one is zero. Determine which number is positive, which is negative, and which is zero, given that \(a b^{2}(a+c)(b+c) < 0\).

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