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

\[ f(x) = \begin{cases} 
x + \arcsin \left( x^2 \sin \frac{6}{x} \right), & \text{if } x \neq 0, \\
0, & \text{if } x = 0 
\end{cases} \]

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