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

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