
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
Based on the definition of the derivative, find \( f^{\prime}(0) \):

\[ 
f(x) = 
\begin{cases} 
\sqrt[3]{1-2 x^{3} \sin \frac{5}{x}} - 1 + x, & x \neq 0 \\
0, & x = 0 
\end{cases} 
\]

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