
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 \( f^{\prime}(0) \):

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

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