
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
Calculate the value of the polynomial $f(x) = 3x^4 - x^2 + 2x + 1$ when $x = 2$ using the Horner's Method:
$$
\begin{cases}
v_0=a_n \\
v_k = v_{k-1} \cdot x + a_{n-k}
\end{cases}
$$
for $k = 1, 2, 3, \ldots, n$. Find the value of $v_3$.

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