
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
Let $g(x) = bx^3 + bx - 3$ for some real number $b$. If $g(g(1)) = 1$, find the value of $b$.
A) $\frac{1}{3}$
B) $\frac{1}{2}$
C) $1$ 
D) $2$

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