
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
**(a)** Sketch the diagram of the function  $f$  if
\[f(x)=4x(1-|x|) , \quad |x| \leq 1.\]**(b)** Does there exist derivative of  $f$  in the point  $x=0 \ ?$ **(c)** Let  $g$  be a function such that
\[g(x)=\left\{\begin{array}{cc}\frac{f(x)}{x} \quad :  x \neq 0 \text{ }  4 \ \ \ \ \quad : x=0\end{array}\right.\]
Is the function  $g$  continuous in the point  $x=0 \ ?$  **(d)** Sketch the diagram of  $g.$ 

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