
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 Rule formula $$\begin{cases} \overset{v_{0}=a_{n}}{v_{k}=v_{k-1}x+a_{n-k}}\end{cases}$$, (where k=1, 2, 3, ..., n) to calculate the value of the polynomial $f(x) = 3x^4 - x^2 + 2x + 1$ when $x=2$; then $v_3 = \_\_\_\_\_\_$.

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