
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 $g(x)$ be a polynomial with leading coefficient 1, whose roots are the reciprocals of the roots of $f(x)=x^3 - ax^2 + bx - c$, and $a, b, c$ are consecutive positive integers such that $a < b < c$, determine $g(1)$ in terms of $a, b,$ and $c$.

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