
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
Use Qin Jiushao's algorithm to find the value of the polynomial \\(f(x)=1-5x-8x^{2}+10x^{3}+6x^{4}+12x^{5}+3x^{6}\\) when \\(x=-4\\). Find the difference between the maximum and minimum values among \\(v\_{0}\\), \\(v\_{1}\\), \\(v\_{2}\\), \\(v\_{3}\\), and \\(v\_{4}\\).

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