
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 the Horner's method to calculate the value of the polynomial \\(f(x)=1+5x+10x^{2}+10x^{3}+5x^{4}+x^{5}\\) at \\(x= -2\\). The value of \\(v_{3}\\) is \_\_\_\_\_\_\_\_

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