
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
The function $f(x) = x^5 + ax^4 - bx^2 + 1$, where $a$ is the decimal number corresponding to $1202_{(3)}$, and $b$ is the greatest common divisor of 8251 and 6105. Use the Horner's method to find the value of $V_3$ when $x = -1$.

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