
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
If \( x_{1}=1, x_{2}=1-\mathrm{i}, x_{3}=1+\mathrm{i} \) (where \( \mathrm{i} \) is the imaginary unit) are the three solutions to the equation \( x^{3}+a x^{2}+b x+c=0 \), then find \( a+b-c \).

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