
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 graphs of four functions, labelled \( A \) through \( D \), are displayed. The domain of function \( D \) is \(\{0, 1, 2, 3, 4\}\). Determine the sum of the labels of the functions which have domain specifications and the product of the labels of the functions which are continuous and invertible. 
- Function \( A \): \( y = \sin(x) \) from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\)
- Function \( B \): \( y = x^3 - x^2 \)
- Function \( C \): \( y = \sqrt{x} \) from \(0\) to \(4\)
- Function \( D \): \( y \) values at \( \{0,1,2,3,4\}\) are \{2, 0, 2, 4, 0\}

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