
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

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

\[ 
f(x) = \begin{cases} 
2x^2 + x^2 \cos \left( \frac{1}{9x} \right), & x \neq 0 \\
0, & x = 0
\end{cases}
\]

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