
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)=7x^5+5x^4+3x^3+x^2+x+2\\) at \\(x=2\\). Let \\(v_0=a_5\\), \\(v_1=v_0x+5\\), ..., \\(v_5=v_4x+2\\). Then, calculate the value of \\(v_3\\).

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