
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
Using the Horner's method, find the value of the polynomial \\(f(x)=7x^{5}+5x^{4}+3x^{3}+x^{2}+x+2\\) at \\(x=2\\). Let \\(v\_{0}=a\_{5}\\), \\(v\_{1}=v\_{0}x+5\\), \\(…\\), \\(v\_{5}=v\_{4}x+2\\). Find the value of \\(v\_{3}\\).

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