
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 $f(x) = ax^3 - 2ax + 3a - 4$ has one zero in the interval $(-1, 1)$.

(1) Find the range of the real number $a$;  
(2) If $a = \frac{32}{17}$, use the bisection method to find the solution of $f(x) = 0$ in the interval $(-1, 1)$, accurate to $0.1$.

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