
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 $f(x) = \ln(ax+1) + x^3 - x^2 - ax$ (where $a \in \mathbb{R}$),
1. If $x = \frac{2}{3}$ is the extremum point of the function $f(x)$, find the value of the real number $a$;
2. If $a = -1$, and the equation $f(1-x) - (1-x)^3 = b$ has real roots, determine the range of the real number $b$.

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