
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
Given the function $f(x)=x^{5}+ax^{4}-bx^{2}+1$, where $a$ is the decimal equivalent of $1202_{(3)}$, and $b$ is the greatest common divisor of $8251$ and $6105$. Use Qin Jiushao's algorithm to find the value of $V_{3}$ when $x=-1$.

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