
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
The function \( f(x) \) is not defined at \( x = 0 \). Determine the value of \( f(0) \) so that \( f(x) \) is continuous at \( x = 0 \), given

\[ 
f(x) = \frac{\sqrt[3]{1+x} - 1}{\sqrt{4+x} - 2} 
\]

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